What Is the Least Common Multiple? A Kid-Friendly Guide

Just like the multiplication table is a building block for so much of the math we do, the least common multiple has its own important role to play.

From adding fractions with different denominators to solving problems with repeating patterns, the LCM shows up across many areas of math.

If you’re just learning about the least common multiple, need a refresher, or are prepping for an exam, this is the guide for you.

We are Mathnasium of West Chester, and we’ll walk you through what the LCM is and how to find it using three easy-to-follow methods, with solved examples, practice problems, and answers to frequently asked questions.

Quick Facts: The Least Common Multiple (LCM)

• What is the least common multiple? The smallest multiple that two or more numbers have in common.

• What does LCM stand for? Least Common Multiple. It's also called the Lowest Common Multiple.

• How do you find the LCM? There are three methods: Listing Multiples, Prime Factorization, and the Division Method.

• Can the LCM be smaller than the numbers you're working with? No. The LCM is always equal to or greater than the largest of the numbers.

• Can two numbers have an LCM that is one of the numbers itself? Yes. This happens when one number is already a multiple of the other.

• Where does the LCM show up in math? Adding and subtracting fractions with different denominators, solving problems with repeating events, and working with algebraic expressions.

Let’s Review: What Is a Multiple?

A multiple of a number is what we get when we multiply the number by whole numbers (1, 2, 3, 4, and so on).

For example:

• The multiples of 3 are: 3, 6, 9, 12, 15, 18, …

• The multiples of 5 are: 5, 10, 15, 20, 25, 30, …

Multiples go on forever, and there's always a bigger one.

📕 You May Also Like: What Is a Product in Math? A Complete Overview 

What Is the Least Common Multiple?

The least common multiple (LCM) of two or more numbers is the smallest multiple they have in common.

Let's see this with 4 and 6:

• The multiples of 4 are: 4, 8, 12, 16, 20, …

• The multiples of 6 are: 6, 12, 18, 24, 30, …

The smallest number that appears in both lists is 12, so the LCM of 4 and 6 is 12.

Here's a way to think about it: 

Imagine two traffic lights. One changes every 30 seconds, the other every 45. At first, they're out of sync, but if you wait long enough, they'll turn green at exactly the same moment. 

That moment happens at 90 seconds, the first time their patterns line up. By then, the first light has switched three times (303=90) and the second twice (45 × 2 = 90). That syncing point is the LCM of 30 and 45.

How Do We Find the Least Common Multiple?

There are three methods for finding the LCM, and some methods will be more efficient depending on the numbers we’re working with.

• Listing Multiples

• Prime Factorization

• Division Method (Ladder Method)

We’ll go through each one step by step so you can choose whichever works best for you!

1. Listing Multiples Method

The listing multiples method is the simplest way to find the least common multiple. It works just like it sounds. We just list out the multiples of each number and look for the smallest one they share.

Let’s see how it works with an example! 

We’ll find the LCM of 6 and 8:

1. List the multiples of 6: 6, 12, 18, 24, 30, 36, …

2. List the multiples of 8: 8, 16, 24, 32, 40, …

3. Find the smallest multiple they both have: 24

So, the LCM of 6 and 8 is 24!

Pretty simple, just like we promised. 

Now, while finding the LCM by listing multiples is quick and easy and helps us visualize everything clearly, it works best with smaller numbers.

However, if we're working with larger numbers like 72 or 124, listing all the multiples can take a while.

But don’t worry, this is just the first method; there are still two more to explore.

2. Prime Factorization Method

The prime factorization method helps us find the least common multiple by breaking numbers down into their prime factors.

And do we remember what prime factors are? Let’s remind ourselves just in case.

A prime number is a number that can only be divided by 1 and itself (like 2, 3, 5, 7, 11, etc.). A prime factor is a prime number that multiplies with others to make a bigger number.

So, instead of listing out multiples, we use prime numbers to build each value from the ground up.

Let’s look at an example to see how this works.

We’ll find the LCM of 48 and 72 using prime factorization:

1. Break each number into prime factors:

48 = 2 × 2 × 2 × 2 × 3 or 2⁴ × 3

72 = 2 × 2 × 2 × 3 × 3 or 2³ × 3²

2. Take the highest power of each prime:

The prime factors we find in 48 and 72 are 2 and 3.

The highest power of 2 is 2⁴ (from 48).

The highest power of 3 is 3² (from 72).

3. Multiply the selected prime factors together:

2⁴ × 3² = 16 × 9 = 144

So, the LCM of 48 and 72 is 144!

This method works well for bigger numbers because we don’t have to list out those long rows of multiples.

3. Division Method (Ladder Method)

The division method, also called the ladder method, is another way to find the LCM where we divide both numbers at the same time using their common factors.

In case you have forgotten, a common factor is a number that divides both numbers evenly. For example, the common factors of 12 and 18 are 1, 2, 3, and 6.

Let’s see how this method would work for finding the LCM for 54 and 90.

1. Write the numbers side by side

We start by writing 54 and 90 next to each other like so:

2. Keep dividing by the smallest common factor until none are left

The smallest number that divides both 54 and 90 is 2, so we divide and write the results below:

Now, both 27 and 45 are divisible by 3, so we divide by 3 next:

Again, both 9 and 15 are divisible by 3, so we divide by 3 again:

Finally, 3 and 5 have no common factors (other than 1), so we stop here. 

3. Multiply all the divisors and remaining numbers

Now, we multiply all the numbers we divided by (2, 3, and 3) and the final row (3 and 5) to get the LCM:

2 × 3 × 3 × 3 × 5 = 270

So, the LCM of 54 and 90 is 270!

The division method works best with numbers that share many common factors because it keeps the process clean and easy to follow.

When two numbers don't share many factors, like 68 and 98, prime factorization tends to be the more effective approach.

Each method has its strengths. The best one to use depends on the numbers in front of you.

📕 You May Also Like: What Is Division in Math? A Simple & Complete Overview

Solved Examples for Finding the Least Common Multiple

Let’s go through a few solved examples together!

Example 1: Listing Multiples Method

Let's try another one together. Find the LCM of 14 and 18.

1. List the multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, …

2. List the multiples of 18: 18, 36, 54, 72, 90, 108, 126, …

3. The smallest number that appears in both lists is 126.

So, the LCM of 14 and 18 is 126.

Example 2: Prime Factorization Method

Let’s find the LCM of 32 and 40 using the prime factorization method.

1. Break each number into prime factors:

32 = 2 × 2 × 2 × 2 × 2 or (2⁵)

40 = 2 × 2 × 2 × 5 or (2³ × 5)

2. Take the highest power of each prime:

The prime factors we find in 32 and 40 are 2 and 5.

The highest power of 2 = 2⁵ (from 32)

The highest power of 5 = 5 (from 40)

3. Multiply the selected prime factors:

2⁵ × 5 = 32 × 5 = 160

So, using the prime factorization method, we found that the LCM of 32 and 40 is 160.

Example 3: Division (Ladder) Method

Let’s find the LCM of 90 and 126 using the division method (ladder method).

1. Write the numbers side by side:

We start by writing 90 and 126 side by side.

2. Keep dividing by the smallest common factor until none are left:

The smallest number that divides both 90 and 126 is 2, so we divide:

Now, both 45 and 63 are divisible by 3, so we divide again:

Both 15 and 21 are still divisible by 3, so we divide again:

Now, 5 and 7 have no common factors other than 1, so we stop here.

3. Multiply all divisors and the remaining numbers

Now, we multiply all the numbers we divided by (2, 3, and 3) and the final row (5 and 7) to get the LCM:

2 × 3 × 3 × 5 × 7 = 630

So, using the division method, we found that the LCM of 90 and 126 is 630!

Your Turn! Check Your Knowledge of Finding the LCM

Ready to practice what we’ve covered? Try these practice problems on your own and check your answers at the bottom of the guide.

1. Find the LCM of 14 and 22 using the listing multiples method.

2. Find the LCM of 36 and 45 using the prime factorization method.

3. Find the LCM of 56 and 72 using the division (ladder) method.

Frequently Asked Questions About the LCM

We know the LCM can bring up a few questions, so we’ve put together clear answers to the ones students ask most often.

1. When do we use the LCM?

We mostly use the LCM for adding or subtracting fractions with different denominators, and for solving problems involving repeating events, such as figuring out when two schedules or patterns will line up again.

2. What is the difference between LCM and GCF?

This trips a lot of students up. The LCM finds the smallest multiple that two or more numbers share, while the GCF finds the largest factor that two or more numbers share. We use the LCM to find common denominators and the GCF to simplify fractions.

3. Can two numbers have an LCM that is one of the numbers itself?

Yes! This happens when one number is a multiple of the other. 

For example, the LCM of 6 and 18 is 18, because 18 is already a multiple of 6.

4. What happens if two numbers have no common factors?

In that case, the LCM of these numbers is simply their product. For example, the LCM of 7 and 9 is 63 (7 × 9), because they share no common prime factors. This happens whenever two numbers are relatively prime, meaning their GCF is 1.

5. Can the LCM of two numbers ever be smaller than both numbers?

No. The LCM is always equal to or greater than the largest of the two numbers. Since we're looking for a shared multiple, the result can never be smaller than either number.

At Mathnasium, specially trained tutors help students build a deep understanding of what the LCM is and how to find it, one step at a time.

Master the Least Common Multiple (And Any Other Math Concept) with Mathnasium

Mathnasium is a math-only learning center dedicated to helping K–12 students of all skill levels learn and master math.

Whether a student needs help (re)building foundational skills, mastering specific concepts like the least common multiple, or a challenge above their curriculum level, we teach for true understanding.

To help students reach that level, we don’t rely on a one-size-fits-all curriculum but on our proprietary teaching approach, the Mathnasium Method™, designed around individual students' needs and learning styles. 

Each student starts their Mathnasium enrollment with a diagnostic assessment that helps us identify their current skills, knowledge gaps, and learning goals. From there, we build a personalized learning plan tailored to their needs.

Our specially trained tutors use a combination of verbal, visual, mental, tactile, and written techniques to help students truly make sense of the math they are working with. 

If students get stuck on a concept like factoring and the LCM, we break it down into manageable steps and teach both the how and the why behind it. Gradually, students learn to do the same independently and walk out of our centers with the problem-solving skills and critical thinking tools they can use in math and beyond.

Fun is an important part of how we work. Sessions often include game-based and hands-on activities that keep students engaged and learning enjoyable. Students earn rewards along the way, and every bit of progress gets celebrated, so confidence grows alongside mastery.

Our method brings measurable results

• 94% of parents report an improvement in their child's math skills and understanding

• 93% of parents report their child's improved attitude toward math after attending Mathnasium

• 90% of students saw an improvement in their school grades

With over 1,100 learning centers, Mathnasium brings structured, personalized math support close to where you live.

For families in and around West Chester, OH, Mathnasium of West Chester is a trusted local resource. Our commitment to student growth has earned meaningful recognition in the community, including:

• 100+ glowing Google Reviews

• Cincy Magazine's 2025 Family's Choice Award for "Tutoring/Learning Center"

• City Beat's 2025 Best of Cincinnati award for "Best Tutoring Center"

If you are looking for structured, patient, and individualized math support for your child, our team is ready to assist.

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Psst! Check Your Answers Here

Great job working through the practice problems! Here are the answers:

1. LCM of 14 and 22 — Listing Multiples Method

• List the multiples of 14: 14, 28, 42, 56, 70, 84, 98, 112, 126, 140, 154, …

• List the multiples of 22: 22, 44, 66, 88, 110, 132, 154, …

• The smallest number that appears in both lists is 154.

The LCM of 14 and 22 is 154.

2. LCM of 36 and 45 — Prime Factorization Method

Break each number into prime factors:

• 36 = 2 × 2 × 3 × 3 or 2² × 3²

• 45 = 3 × 3 × 5 or 3² × 5

Take the highest power of each prime:

• The highest power of 2 is 2² (from 36)

• The highest power of 3 is 3² (from both)

• The highest power of 5 is 5¹ (from 45)

Multiply the selected prime factors together:

2² × 3² × 5 = 4 × 9 × 5 = 180

The LCM of 36 and 45 is 180.

3. LCM of 56 and 72 — Division (Ladder) Method

Write the numbers side by side: 56 and 72

Divide by the smallest common factor and keep going until no common factors remain:

• 56 and 72 are both divisible by 2 → 28 and 36

• 28 and 36 are both divisible by 2 → 14 and 18

• 14 and 18 are both divisible by 2 → 7 and 9

• 7 and 9 have no common factors, so we stop here

• Multiply all the divisors and the remaining numbers:

2 × 2 × 2 × 7 × 9 = 504

The LCM of 56 and 72 is 504.

How did you do?