## The Lesson

The least common multiple of two or more numbers can be found. Imagine we wanted to find the least common multiple of 3 and 4.

## How to Find the Least Common Multiple

Finding the least common multiple is easy.

## Question

What is the least common multiple of 3 and 4?

# 1

List the multiples of 3.
Multiples of 3 = 3, 6, 9, 12, 15...
Don't forget: The multiples of 3 are the result of multiplying 3 by successive integers: 3 × 1 = 3, 3 × 2 = 6...

# 2

List the multiples of 4.
Multiples of 4 = 4, 8, 12, 16, 20...

# 3

The smallest multiple that appears in both lists is the least common multiple.

Multiples of 3 = 3, 6, 9, 12, 15...

Multiples of 4 = 4, 8, 12, 16, 20...

12 is the least common multiple of 3 and 4.

## Lesson Slides

The slider below gives another example of finding the least common multiple and an example of why it is useful.

## What's in a Name?

The least common multiple (LCM) is so called because it is the smallest (least) multiple that is the same (common) to the numbers.

## What Is a Multiple?

A multiple is the result of multiplying a number by an integer (a whole number). For example, the multiples of 3 are:
3, 6, 9, 12, 15
• 3 is the result of multiplying 3 by 1.
• 6 is the result of multiplying 3 by 2.
• 9 is the result of multiplying 3 by 3.
• 12 is the result of multiplying 3 by 4.
• 15 is the result of multiplying 3 by 5.

## What Is the Least Common Multiple?

The Least Common Multiple is the smallest multiple that is common to two or more numbers.