Teaching least common multiple methods can feel like you’re juggling three balls at once. This is especially true when you’re trying to help your students understand which strategy to use and when. If you’ve ever wondered how to walk through LCM with your students clearly, or if you just want a fresh approach, this post is for you. I’m sharing two short videos that walk you through the core concepts behind the least common multiple methods. I also show how to apply them to real-world word problems. Whether you’re brand-new to teaching LCM or just looking to sharpen your explanations, you’ll walk away feeling more prepared, and your students will too.

Watch These Least Common Multiple Methods Videos

If you’re teaching least common multiple methods and want your students to really get it, these two quick videos walk through everything you need. The first one breaks down three different ways to find the least common multiple. We go over how to list multiples, use prime factorization, and the ladder method. I explain how each one works and show you where your students typically get stuck. Then, I help you think through which method might click the best depending on the problem at hand.

The second video zooms in on a real-world LCM word problem. You’ll see how I model problem-solving by drawing visuals, listing out steps, and using different methods to get the same answer. It’s the kind of flexible thinking we want to build in our students. It’s a great refresher if you’re prepping to teach this skill or want a new way to explain it. Both videos give you practical examples, teaching tips, and clarity. This way, you can walk into your next LCM lesson with confidence.

Extra Tip: Let Students Choose Their Method

Here’s a tip I’ve learned from teaching least common multiple methods over the years. After modeling all three, encourage your students to try each one a few times, then reflect on which method feels most natural to them. When your students take ownership of their problem-solving strategies, they’re more likely to stay engaged and get the answer right!

Also, revisiting LCM is a must when working with fractions. This concept pops up again and again, especially when adding or comparing fractions with unlike denominators. Having that solid foundation early on makes everything easier later in the year.

Resources to Reinforce Least Common Multiple Methods

Once you’ve taught the different methods, it’s time for your students to get some hands-on practice. That’s where your resource choices really matter. In my TPT store, you’ll find engaging LCM activities that provide excellent notes and practice.

There’s a math doodle wheel that helps your students visualize and organize their steps, a color-by-number activity that makes practice more engaging, and a set of doodle notes on the ladder method. These are great for classwork, stations, early finisher bins, or even small group instruction.

Save for Later

Want to come back to this post when you’re prepping your LCM lessons? Be sure to pin this so you’ll have all your least common multiple methods and strategies in one place when you need them!

The post Finding Least Common Multiple: Methods That Actually Click With Kids appeared first on Cognitive Cardio Math.

When you’re teaching the greatest common factor to 6th graders, it helps to have a clear structure and multiple methods at your fingertips. Whether you’re brand new to teaching this concept or just want a more effective way to deliver it, this post has you covered. I’ve pulled together two videos and a helpful classroom resource that will take the guesswork out of introducing and practicing GCF.

Greatest Common Factor Videos With Three Strategies That Work

In this first video, I explain what the greatest common factor actually means. Then, we walk through three go-to strategies to find it. We look at listing factors, using prime factorization, and my favorite, which is the ladder method. I show you how to help your students decide which method is best for the numbers they’re working with. I also weave in divisibility rules and factor trees to give your students extra tools for breaking down numbers. Each strategy builds a deeper understanding of how numbers connect. This helps to make the greatest common factor more than just a vocabulary term. It becomes something your students can use.

3 Ways to Find the Greatest Common Factor

Solving GCF Word Problems

Once your students understand how to find the GCF, it’s time to show them how to apply it. In the second video, I walk through a word problem that requires using GCF. I model how your students can organize their thinking, use a guess-and-check strategy if they feel stuck, and connect the numbers in the problem back to what they already know about factoring. We also solve the problem using the ladder method, allowing your students to see how math shows up in everyday problem-solving. This is a great way to answer the classic “When are we going to use this?” question.

Help Students Choose What Works With These Three GCF Strategies

When it comes to teaching the greatest common factor, it’s not just about memorizing the steps. It’s about helping your students understand why each method works and when to use it. Let’s take a closer look at the three strategies highlighted in the video and resource.

Listing Factors is a solid place to start with smaller numbers. You should always encourage your students to list pairs in order (starting with 1 and the number itself) and to stop once they meet in the middle. It’s simple and visual, but it can be tricky when working with larger numbers, especially if your students don’t know all their math facts.

Prime Factorization takes things a step further by using factor trees to break numbers into their prime parts. This method gives your students a way to actually see how numbers are built. They learn how to find what factors two numbers have in common. It’s a great strategy for reinforcing prime numbers and multiplication facts, too.

The Ladder Method is typically students’ favorite! It feels less messy than factor trees and works well with large numbers. You pull out common factors on the side and divide both numbers until there’s nothing left to pull out. It’s straightforward, systematic, and pairs beautifully with visual learning styles. Plus, once your students master it, it becomes their go-to method for both GCF and least common multiple later on.

Greatest Common Factor Resource

To go along with the videos, I’ve created a classroom resource packed with everything you need to teach the greatest common factor from start to finish. The resource includes print and digital versions of GCF notes and practice pages, plus two exit tickets that help you assess understanding right away. Each strategy, listing factors, prime factorization, and the ladder method, has its own dedicated lesson page and step-by-step examples.

Your students can also get a chance to try each method on their own with guided support. There’s a Fold It Up activity that helps solidify how to use GCF and when to apply it. Whether you’re teaching a whole group, a small group, or assigning it digitally, this set is built for flexibility and clarity. Your students will walk away knowing how to find the GCF and why it matters.

Help Students Master the Greatest Common Factor

Teaching the greatest common factor in 6th grade math doesn’t have to be complicated. With the right mix of visuals, guided examples, real-life application, and supportive practice, your students can truly understand and use GCF consistently. Whether you start with the videos, the printables, or both, you’ll set them up for success in future algebraic thinking and number sense.

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Remember to save this post to your favorite math Pinterest board for quick access to these greatest common factor resources!

The post 3 Ways to Find Greatest Common Factor and Finding GCF Word Problem appeared first on Cognitive Cardio Math.

When I was in the classroom, I was always on the lookout for ways to make math concepts more engaging. One topic that could sometimes trip my students up was the least common multiple (LCM). While the concept itself isn’t all that difficult, keeping my students engaged long enough to master it? Sometimes that was another story. Over time, I found that using a combination of methods, like the ladder method, the listing method, and prime factorization, helped my students grasp the concept from different angles. Today, I’m sharing two resources that were my go-to for making this topic approachable and engaging for my students.

Least Common Multiple in the Real World

One of the best ways I found to make the least common multiple more meaningful to my students was to show them how it applies to real-life situations. After all, math isn’t just about solving problems on a worksheet. It’s about recognizing patterns and making sense of the world around us.

Below are some of my favorite real-world applications of least common multiple that helped my students see why this concept matters:

• Scheduling Events: If two events happen on different cycles, like a student who has soccer practice every 4 days and piano lessons every 6 days, how do you figure out when they’ll both land on the same day? By finding the least common multiple of 4 and 6, students can determine when both activities will line up.
• Stocking Supplies: Suppose a grocery store receives milk deliveries every 3 days and bread every 5 days. To figure out when both deliveries will arrive on the same day, you’d find the least common multiple of 3 and 5.
• Buying in Bulk: If hot dogs come in packs of 10 and buns come in packs of 8, how many packs should you buy to have the same number of both? The least common multiple of 10 and 8 gives the answer 40. You’d need four packs of hot dogs and five packs of buns to have an equal number.

I loved weaving these examples into our least common multiple lessons because they gave my students an “aha!” moment. Suddenly, they weren’t just memorizing a math skill. They were seeing how math helps solve everyday problems.

Two Ways to Find the Least Common Multiple

In my classroom, I taught my students three different ways to find the least common multiple, but today we’ll focus on two of them. I always found that different students would catch on with one way or another. By teaching them three methods, I could make sure that everyone found a strategy for finding LCM that they felt comfortable with.

1. Ladder Method

One of my favorite techniques for finding the least common multiple was (and still is!) the ladder method. My students worked through problems using a step-by-step process using a visual that kind of looks like a ladder. In this method, students break down numbers into their prime components and then combine some of those factors to get the least common multiple. This visual approach helped many students see the “building blocks” of numbers and understand how different factors come together.

I explore this method in more detail in my Using the Ladder Method in Middle School Math blog post. You can also find more information about this technique in Three Ways to Use Prime Factorization in Middle School or this short LCM video (this and some of the other videos on my YouTube channel are early morning Facebook lives:-). There are also videos on my channel for the other LCM methods.)

2. Listing Method

Another strategy that proved effective was the listing method for finding the least common multiple. I had my students list multiples of each number until they found a common multiple. This approach is great for reinforcing the concept of multiples and shows students the practical side of math.

By connecting this concept to multiplication, something my students were already familiar with (or should be!), they were more open to jumping into something that they deemed “difficult.” This method’s simplicity can make it an excellent starting point for discussing more complex ideas later. It’s great to see the moments when students excitedly point out the common number they’ve spotted. A small victory that builds their confidence!

However, one thing I don’t love about this method is that students might skip multiples, list incorrect multiples, or not list enough multiples and not find the correct LCM. Sometimes, if the LCM is very large, students have to list and list and list until they find it. These types of situations can lead to frustration which is why I always equip them with other options.

How I Taught Finding the Least Common Multiple

When it came to teaching least common multiple, I quickly learned that the more interactive the lesson, the better my students understood and retained the concept. While I introduced LCM through direct instruction and practice problems, I knew I needed activities that would keep my students engaged while reinforcing their learning.

That’s where visual resources like the LCM Math Doodle Wheel and the Least Common Multiple Color by Number activities made all the difference. These two activities turned what could have been routine practice into something fun, creative, and effective.

Let’s take a look at how each one works and how they can help your students master the least common multiple in a way that sticks!

Using a Doodle Wheel to Introduce LCM

I introduced the students to the concept of finding the least common multiple using the LCM Doodle Wheel. This interactive note-taking resource has always been a favorite of students. They really love how it breaks everything down into simple components and steps. This makes it easier to understand and creates a great reference tool they refer back to as needed. Plus. . . the ability to add color and doodles helps the concepts stick in their mind.

Vocabulary and Definitions

When introducing this topic, I always start by defining LCM and what it means. The first wedge of the wheel is the perfect place to add key vocabulary and definitions that students will need to know.

I always include the terms ‘least common multiple’ and ‘multiple’ so I can make sure we are all on the same page. This allows me to use these terms going forward and reduces the chance of misunderstandings. In addition to the definition, you can also add an example in this space.

The List Method

Next up, we move to the wheel section that focuses on the List Method. Using the list method, students will tap into their multiplication skills. They will make a list of the multiples of the numbers they’re finding LCM for. I usually suggest that they start with listing 5-6 multiples. If they don’t find a match, they can keep going.

Using the List Method, students are looking for the smallest multiple that all the target numbers have in common. For example, when finding the multiples of 9 and 6, we can see that both 18 and 36 are in both lists. However, since we are looking for the LEAST common multiple, we want the smallest one – so 18 is the answer.

I always encourage students to start with the multiples of the larger target number. Then, when working on the smaller number, they can stop when they find the first common multiple.

The Ladder Method

I typically taught my students about the Ladder Method at the start of the school year. Then we applied it to different concepts as we came to them in the curriculum. The Ladder Method gets students working with prime factors. While this may be perceived as more difficult by students at the start, it is often the faster, more ‘dependable’ way to find the least common multiple. I have found that through modeling and explaining my thinking, students pick up this method fairly quickly.

We started by discussing why the ladder method is useful for finding the least common multiple. I would explain to students that this method was usually quicker than the list method, and left less room for errors.

When introducing this method I would connect it with students skill of division. We would start by finding a number that both target numbers could be divided by. We write that number to the side and then we divide. The quotients are written at the bottom of the ladder, as seen in this image.

Once we are done dividing, it is time to ‘ignore’ the numbers in the ladder and just multiply all the numbers on the side and bottom of the ladder. That answer is the least common multiple.

Putting it Into Action

The final section of the wheel is designed for practicing what students learned. Using the provided word problem, we walked through both the list method and the ladder method together. This way students could see both methods in action and how they reached the same answer.

It was not uncommon for students to start choosing a preferred method by the time we finished up the wheel. I always explained that in class, unless told otherwise, they could use either method. However I did encourage them to use the other method as a way of checking their answer.

With the wheel sections completed, we dove into the practice problems around the outside edge of the wheel. My students then kept their wheels in their math notebooks. I encouraged them to refer back to them whenever they worked on LCM problems. This way, they weren’t just memorizing steps. They were actively engaging with the method in a way that helped them internalize the concept.

Practicing LCM With Color By Number

One of the best ways I found to make practicing least common multiple more engaging was my Least Common Multiple Color by Number activity. My students always responded well to activities that felt more like a game than a worksheet. This resource combined problem-solving with creativity in a way that kept them motivated.

After teaching the concept of least common multiple, I would assign this activity as an independent or small-group task. Each student worked through a set of LCM problems. They would solve for the correct answers and match them to a color-coded key. Once they had their answers, they colored in the corresponding sections of the picture. If they solved everything correctly, they ended up with a fully colored image. This immediate visual feedback was a great motivator! If their picture didn’t look right, OR if their answer wasn’t the sheet, they knew to go back and check their work!

I loved that this activity allowed for easy differentiation. Some of my students needed more challenge, while others benefited from simpler problems. One of the biggest benefits of this activity was the inclusion of word problems that showed how the least common multiple applies to everyday life. My students loved the scheduling and purchasing scenarios because they could see why this matters outside of math class. Whether they were figuring out when two events would overlap or how many packs of supplies to buy, these problems helped them connect math to real-world thinking.

Making the Least Common Multiple Stick

Looking back, the key to helping my students truly understand the least common multiple was making it both visual and interactive. The LCM Doodle Wheel was the perfect way to introduce the topic and strategies in a way that made them easy to understand. The Least Common Multiple Color by Number gave them a fun, low-pressure way to practice while reinforcing real-world applications. By combining these activities, my students built confidence in their ability to find the LCM, and they even enjoyed the process along the way!

If you’re looking for ways to bring LCM to life in your classroom, I highly recommend trying these resources. Whether through coloring, note-taking, or hands-on practice, giving your students a mix of structured guidance and creative engagement makes all the difference.

Save for Later

Remember to save this post to your favorite math Pinterest board for quick access to these least common multiple resources!

The post Finding the Least Common Multiple: Effective Teaching Ideas appeared first on Cognitive Cardio Math.

Are you teaching fraction operations in middle school (or reteaching fraction concepts when they pop up in middle school?)

Are you always looking for fraction content or fraction teaching tips?
I’m here to help! I’ve decided to do something I’ve never done on my blog:

• Since I have so many fraction-related posts for upper elementary and middle school math, I’ve added a couple of new ‘summary’ posts as a kind of index.
• One post (this one) will include posts about teaching fraction concepts, and the other will summarize the posts about fraction games and activities. 

​So, let’s get to the fraction content posts.

The first and newest is the series of foundational fraction posts.

• Many of these posts include a free download or two. You can access the downloads by registering for the free Fraction Review Toolkit.

The posts in the fraction operations series include: 

1) Teaching Fractions in Middle School: Reviewing the Basics

• In this post, we talk about the need that always seems to pop up – the need to review certain fraction concepts before moving on to your specific fraction curriculum.
• We review the meanings of fraction terms, how to represent fractions, and a few ways to weave fractions into class even when you aren’t teaching fraction concepts.

2) Teaching Fractions in Middle School: Using Models

• This post addresses the progression of fraction skills through the elementary grades up to 5th grade (and beyond).
• I share a few examples of using fraction models when adding and subtracting fractions and explore a combination of number lines & fraction strips.

3) Teaching Fractions: Benchmarking and Estimation

• As the title indicates, this post focuses on using benchmarks, explores the 4th grade benchmark standard, and includes examples of how to use estimation when adding fractions.

4) Teaching Fraction Operations in Middle School: Finding Equivalent Fractions

• Equivalent fractions are in many situations, and we look at several of these in this post.
• We look at three ways to find common denominators in order to create equivalent fractions, and we explore representations of equivalent fractions.

Fraction Operations in Middle School Content

In addition to the fraction series, I’ve written a few other fraction-related posts over the past several years.

Using the Ladder Method to Find LCD

This method of finding the least common denominator is a favorite of mine because it includes the ladder method. It outlines the steps for finding the least common denominator and explains how this method has been helpful to students.

Fraction Division…Another Way

This post focuses on teaching fraction division using the common denominator method, explaining why this method works, and explaining how my 6th grade students respond to the method.

Teaching Multiplication of Fractions and Mixed Numbers

• Multiplying mixed numbers can be tricky! Breaking it down with students can be so much fun.
• This post shares a common mistake students make, explains the numerical ‘breakdown’ of a problem, and shows the breakdown using different representations.

Why NOT use the butterfly method when adding and subtracting fractions?

• I’ve had some pretty interesting experiences with the butterfly method in 6th grade math. This post shares how I learned about this method and how my students used it.

Want even more (there’s so much more!) fraction and fraction operation content and materials all in one place?
Check out the program Fractions: From Foundations to Operations.

The post Fractions and Fraction Operations in Middle School Math appeared first on Cognitive Cardio Math.

Do you use the ladder method in middle school or elementary math, to find GCF, LCM, or for any other math concepts?

If you haven’t had the chance to use the ladder method (or the upside down birthday cake method, as some call it), I highly recommend it.

It can be used for several different concepts and has some great benefits for students.

 

What Concepts Can the Ladder Method Be Used With?

The ladder method can be used for quite a few concepts. As you can see in the anchor chart below (sorry it’s not as pretty as some!), upper elementary and middle school math students can use the ladder method for:

• finding greatest common factor (GCF)
• finding least common multiple (LCM)  
• factoring
• finding lowest terms fractions 
• finding prime factorization
• finding the least common denominator (not pictured, but you can read about it in the linked post)! 

Benefits of Using the Ladder Method

1) What I really love about this method is that the process is the same for each use; the outside numbers are just used differently. 

I love the fact that the continually using the ladder method (for various math concepts) leads middle school math students to make greater connections between concepts. Finding factors also seems to come more easily.

2) In addition to helping math students find GCF and LCM, using the ladder method helps students see the relationships between numbers more clearly. 

It’s very easy to see what factors the numbers have in common and how those factors ‘contribute’ to the LCM or GCF.

Using the Ladder Method for Factoring

When I started using the ladder method for factoring,  students picked up the factoring concept MUCH more quickly than when I hadn’t used it.

The steps to use the ladder method for factoring are:

1. Put the expression into the ladder.
2. Take out the common factors, one at a time (common factors go outside the ladder, then divide each number in the expression by that factor and put the quotient below the numbers in the ladder.) 
3. Repeat until all common factors have been ‘removed.’
4. Multiply the numbers on the left of the ladder – this is the GCF, which goes outside the parenthesis in the factored expression.
5. Put the numbers at the bottom of the ladder into the parenthesis.

You can see this process shown on the Fold It Up below.

Ladder Method Resources

Several years ago, I wrote a guest post about the ladder method on the Minds in Bloom blog, so if you’re interested in reading more, check it out here. 

I shared a ladder method fold-it-up in my guest post, but you can also select the button below, if you’d like to download it.

Download the Fold It Up

Ladder Method Doodle Notes

I’ve also created a fun Doodle Notes page to help students with the Ladder Method!

If you’ve used the ladder method before, I’m sure you understand why I love it:-)

If you haven’t used the ladder method yet, I hope you’ll give it a try!

See the Doodle Notes on TPT

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