Question

What is the least common multiple of #{120, 130, 144}?

Answer 1

`9360`

Explanation:

Let us start by finding the prime factorisations of each of the numbers:

`120 = 2 xx 2 xx 2 xx 3 xx 5`

`130 = 2 xx 5 xx 13`

`144 = 2 xx 2 xx 2 xx 2 xx 3 xx 3`

So the smallest number that contains all of these factors in these multiplicities is:

`2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 5 xx 13 = 9360`

If you don't have a calculator to hand, an easier way to do that last multiplication might be:

`2 xx 2 xx 2 xx 2 xx 3 xx 3 xx 5 xx 13`

`=13 xx (3 xx 3) xx 2 xx 2 xx 2 xx (2 xx 5)`

`=13 xx 9 xx 2 xx 2 xx 2 xx 10`

`=13 xx (10 - 1) xx 2 xx 2 xx 2 xx 10`

`=(130 - 13) xx 2 xx 2 xx 2 xx 10`

`=(117 xx 2) xx 2 xx 2 xx 10`

`=(234 xx 2) xx 2 xx 10`

`=(468 xx 2) xx 10`

`=936 xx 10`

`=9360`