Question

How do you make a list of possible pairs of numbers that have a LCM of 48?

Answer 1

`14` such pairs, which are `(1,48),(2,48),(3,48),(4,48),(6,48)`

`(8,48),(12,48),(16,48),(24,48},(48,48),(3,16),(6,16),(12,16),(24,16)`

Explanation:

First of all pairing `48` with all of its factors i.e. `{1,2,3,4,6,8,12,16,24,48}`. This gives us `10` such pairs.

We can also add `(3,16)`, as they are relatively coprime. Further, selecting multiples of `3` will also lead to the pairs `(6,16),(12,16),(24,16)`

Hence in all `14` such pairs, which are

`(1,48),(2,48),(3,48),(4,48),(6,48),(8,48),(12,48),(16,48),(24,48},(48,48),(3,16),(6,16),(12,16),(24,16)`