Greatest Common Multiples

Question

A clock shop has three cuckoo clocks on display. The cuckoos appear at different time intervals. One comes out every 5 minutes, one comes out every 25 minutes, and one comes out every 60 minutes. If they all appear at 5 o'clock, what is the next time they will all come out together?

Answer 1

5 = 5

25 = 5²

60 = 5(3)(2²)

LCM = 2²(3)(5²) = 300 minutes

The cuckoos will all appear simultaneously 300 minutes after 5 PM. That is, at 10 PM.