Hi Aris.

We have to assume the teacher is distributing the sweets evenly (the same number to each student).

If she distributes 6 candies per student, she has none left, so the number of candies is a multiple of 6.

Similarly, the number of candies is a multiple of 8 and of 9.

So you are looking for the lowest common multiple of 6, 8 and 9 which is above 100.

One way to find it is to first find the lowest common multiple under 100 by examining the prime factors:

6 = 2 x 3
8 = 2 x 2 x 2
9 = 3 x 3

So the lowest common multiple has at least three factors of two and two factors of three:

LCM = 2³ x 3² = 72.

Any common multiple of 6, 8 and 9 must be a multiple of 72.

Can you take it from here?

Cheers,
Stephen La Rocque.