Question

There is a group tour at the museum every 20 minutes. A movie about the exhibit begin every 45 minutes. Both begin at 9am. What time will both tour and movie begin at the same time again

Answer 1

This question is best answered by finding the least common multiple of both 45 and 20.  If a scenario indicates every so many, it would be like listing the multiples.  It can be harder to list the multiples of bigger numbers (45, 90, 135, 180 and 20, 40, 60, 80, 100, 120, 140, 160, 180), so another strategy is to use prime factorizations.  The prime factorization of 45 is 3 x 3 x 5 and the prime factorization of 20 is 2 x 2 x 5. The numbers that are the same in both prime factorizations are part of your answer.  All other numbers (the italicized ones) also become a factor in your final answer, so 5 x 3 x 3 x 2 x 2 = 180.  This means 180 minutes later they both start again at the same time.  So 3 hours from 9 am is 12 noon.