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.

Lesson Slides

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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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See Also

What is the least common multiple? What is a multiple?