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# Finding the Least Common Multiple

(KS2, Year 5)

## 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?## Step-by-Step:

# 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...## Answer:

**12**is the least common multiple of 3 and 4.

## 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.**Help Us To Improve Mathematics Monster**

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