The product of a set of distinct positive integers is 140. What is their least possible sum?

The integers must be 4, 5 and 7....since 4 * 5 * 7 =  140.....so the sum is 16

If there were only 2 integers, the least sum would be 24.....  (14 *10)

And there could not be 4 (or more) distinct integers since 140 factors as 2 * 2 * 5 * 7