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.