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# What is the lowest common multiple? We explain what the lowest common multiple is and give examples of how the concept might be taught to your primary school child.

## What is the lowest common multiple?

The lowest common multiple of two numbers is the smallest whole number which is a multiple of both. Teachers may introduce this concept to more able Year 6 children. Quick reminder: a multiple is a number that can be divided by another number a certain number of times without a remainder.

## How to find the lowest common multiple

The basic rule is to list the multiples of the larger number and stop when you get to a multiple of the smaller number. For example:

What is the lowest common multiple of 3 and 8?

Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24...

Multiples of 8 are 8, 16, 24, 32, 40...

So the lowest common multiple of 3 and 8 is 24.

A more difficult challenge may be to ask for the lowest common multiple of a group of three or four numbers.

For example:

What is the lowest common multiple of 6, 15 and 20?

• Start writing out the multiples like this:
• Multiples of 6 are 6, 12, 18, 24, 30, 36
• Multiples of 15 are 15, 30, 45, 60
• Multiples of 20 are 20, 40, 60, 80
• Both 6 and 15 have multiples of 30, however 20 cannot have  a multiple of 30. Both 15 and 20 have a multiple of 60. I know that 6 also has a multiple of 60, because 6 x 10 = 60.
• Because 60 is the only multiple all three numbers have in common, 60 is the lowest common multiple of the three numbers.