SOLUTION: 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

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
RELATED QUESTIONS
One bus route takes 25 minutes and the other bus route takes 55 minutes both buses leave... (answered by josmiceli)

Bus A takes 21 minutes to complete its route. Bus B takes 35 minutes to complete its... (answered by josmiceli)

two buses arrive at the central avenue bus stop at 8 a.m. the route for the city loop bus (answered by ikleyn)

Alesia,Ryan, and Chris began running around a circular track at the same time, from the... (answered by josmiceli)

Trains on the Glasgow Subway depart every 4 minutes, and a complete circuit takes 24... (answered by ikleyn)

Alex's bike ride to work usually takes 22 minutes at 9 kph. One morning he found a new... (answered by Theo,MathTherapy)

There is a circular path around a sport field. Geeta takes 20 minutes to drive one round... (answered by stanbon)

In NYC, the A train takes 28 minutes to return to the station. The B train takes 42... (answered by ikleyn)

You are at a train station one mile from your home. You can walk at a speed of 4 mph. The (answered by rwm)