Question

Find the smallest integer for which `756k` is a multiple of `1584`?

Answer 1

The smallest integer `k` could be is `44` so that `756k` is a multiple of `1584`.

Explanation:

The factors of `756` are

`756=2xx2xx3xx3xx3xx7` and

factors of `1584` are

`1584=2xx2xx2xx2xx3xx3xx11`

As `756k` is a multiple of `1584`, it must have at least - two additional `2s` and one additional `11`.

Hence, `k` should be minimum `2xx2xx11=44` so that `756k` is a multiple of `1584`.