How to Find Least Common Multiple? (+FREE Worksheet!)

The Least Common Multiple (LCM) of a set of numbers is the smallest positive number that is a multiple of all the numbers in the set. Here, we teach you how to find the Least Common Multiple of two or more numbers in a few easy steps.

Watch this practice video for additional examples and reinforcement:

Related Topics

• How to Find the Greatest Common Factor (GCF)
• How to Factor Numbers
• How to Order Integers and Numbers

Step by step guide to finding the Least Common Multiple

Two ways to find the Least Common Multiple are:

1- Using the multiplication to find the Least Common Multiple (LCM)

• Step 1: To find the Least Common Multiple of a set of numbers, write each of the numbers in that set along with a list of the first multiples.
• Step 2: The Least Common Multiple is the first number in all lists.

Note: When looking for the Least Common Multiple of two numbers, start by writing a list of multiples of the larger number, but stop writing this list when the number of multiples you have written is equal to a smaller number. Then start writing a list of smaller multiples until one of them matches the second list.

This method works well, especially when you want to find The Least Common Multiple between two numbers, but it may take longer if you have more numbers.

The Absolute Best Books to Ace Pre-Algebra to Algebra II

2- Use the prime factors to find the Least Common Multiple (LCM)

• Step 1: List the prime factors of each number.
• Step 2: In each list, underline the items that are most duplicated.
• Step 3: Multiply all the numbers you’ve underlined. The answer is the Least Common Multiple.

Least Common Multiple For education statistics and research

Solution:

Pre-Algebra for Beginners 2026 The Ultimate Step by Step Guide to Preparing for the Pre-Algebra Test

Download

$27.99 Original price was: $27.99.$17.99Current price is: $17.99.

Rated 4.30 out of 5 based on 105 customer ratings

Satisfied 92 Students

Multiples of \(8\): \(8, 16, 24, 32, 40, …\)
Multiples of \(6\): \(6, 12, 18, 24, 30, …\)
LCM \(=24\)

Least Common Multiple, Example 2:

Find the LCM for \(4\) and \(12\).

Solution:

Multiples of \(4\): \(4, 8, 12, 16, 20, …\)
Multiples of \(12\): \(12, 24, 36, 48, 60, …\)
LCM \(=12\)

Least Common Multiple, Example 3:

Find the LCM for \(3\) and \(4\).

Solution:

Multiples of \(3\): \(3, 6, 9, 12, 15, 18, …\)
Multiples of \(4\): \(4, 8, 12, 16, 20, 24, …\)
LCM \(=12\)

The Best Book to Help You Ace Pre-Algebra

Least Common Multiple, Example 4:

Find the LCM for \(9\) and \(12\).

Solution:

Multiples of \(9\): \(9, 18, 27, 36, 45, …\)
Multiples of \(12\): \(12, 24, 36, 48, 60, …\)
LCM \(=36\)

Exercises for Finding Least Common Multiple

Least Common Multiple

Find the LCM for each number pair.

• \(\color{blue}{4,14}\)
• \(\color{blue}{5,15}\)
• \(\color{blue}{16,10}\)
• \(\color{blue}{4,34}\)
• \(\color{blue}{8,3}\)
• \(\color{blue}{12,24}\)

Download Least Common Multiple Worksheet

Answers

• \(\color{blue}{28}\)
• \(\color{blue}{15}\)
• \(\color{blue}{80}\)
• \(\color{blue}{68}\)
• \(\color{blue}{24}\)
• \(\color{blue}{24}\)

The Greatest Books for Students to Ace the Algebra