Question

A Box of marbles can be shared equally among 6, 7, or 8 students with 4 marbles left over each time what is the least possible number of marbles in the Box

Answer 1

So the problem is, what is the least number than can be divided into 6, 7 and 8?

The numbers have only one non-1 divisor in common: both 6 and 8 are divisible by 3.

So for our drives we can "delete" one 2 and ask:


what is the smallest number than can be divided into 3,7 and 8 ?

There are no more divisors in common, so we just have to multiply them: 3*7*8 = 21*8=168


and the 4 marbles "extra"? We add them to this sum.


So, the smallest possible number in the box is 168 + 4 = 172.