Question

What is the least common multiple of `{9, 36, 25, 45}`?

Answer 1

`900`

Explanation:

Given: `{9, 36, 25, 45}`

First find the prime factorisations of all of the numbers:

`{ (9 = 3 xx 3), (36 = 2 xx 2 xx 3 xx 3), (25 = 5 xx 5), (45 = 3 xx 3 xx 5) :}`

The smallest number that contains all of these prime factors in the multiplicities in which they occur in each of these numbers is:

`2 xx 2 xx 3 xx 3 xx 5 xx 5 = 900`

So this is the least common multiple.