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Finding the Least Common Multiple
(KS2, Year 5)

homearithmeticfinding the least common multiple
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.

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.
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This page was written by Stephen Clarke.

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