A clock that chimes every p minutes and another clock that chimes every q times chime at the same time. If p and q are two distinct numbers, what is the least number of minutes that must elapse before the two clocks again chime at the same time?

Question

anonymous · Answer

I think it is pq but not sure

mathstudent55 · Answer

It's the LCM of p and q.

anonymous · Answer

I know that part. IS the lcm of p and q pq?

mathstudent55 · Answer

It's only pq if they are mutually prime. If not, then it isn't.

For example, 4 and 9 have no common factors together. 
Multiples of 4: 4, 8, 12, 16, 20, 24, 28, 32, 36, 40, 44, ...
Multiples of 9: 9, 18, 27, 36, 45, ...
The first common multiple of both (the LCM) is 36, which is 4 x 9

But now look at 6 and 9
Multiples of 6: 6, 12, 18, 24, 30, 36, ...
Multiples of 9: 9, 18, 27, 36, 45, ...
LCM is 18, and 18 is not 6 x 9
Since 6 = 2 x 3, and 9 = 3 x 3, and they have a factor in common, the LCM is not pq