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.
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