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

1 Answer
Nov 28, 2016

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.