Question 908935: 3 buses leave a central station at 7am for a continuous circular route. One takes 8 minutes, one takes 9 minutes, and one takes 15 minutes. What time will they all arrive together at the central station?
Answer by JulietG(1812)   (Show Source):
You can put this solution on YOUR website! You're looking for the least common multiple.
Bus A arrives at the station at these minutes: 8, 16, 24, 32, 40, 48, 56, 64, 72, 80, 88, 96, etc
Bus B arrives at the station at these minutes: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90, 99, etc
Bus C arrives at the station at these minutes: 15, 30, 45, 60, 75, 90, etc
Take each of the "minutes" down to their prime factors.
A (8) = 2 * 2 * 2
B (9) = 3 * 3
C (15) = 5 * 3
You'll need to use 3-2s and 2-3s and 1-5 in order to accommodate them all.
2 * 2 * 2 * 3 * 3 * 5 = 360
Bus A will make 45 loops
Bus B will make 40 loops
Bus C will make 24 loops
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