What is the lowest common multiple?

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.
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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.