



 
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:
So the lowest common multiple has at least three factors of two and two factors of three:
Any common multiple of 6, 8 and 9 must be a multiple of 72. Can you take it from here? Cheers,  


Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences. 