An “A” train leaves a subway station every 10 minutes. An “B” train leaves every 12 minutes. An "C" train leaves every 15 minutes. If all trains just left the station on parallel tracks, when will they arrive at the station together again?
you want to find the least common multiple of the times.
10 = 2*5
12 = 2^2 * 3
15 = 3*5
the LCM will have the highest power present for each prime factor
LCM(10,12,15) = 2^2 * 3 * 5 = 60
hey i have no idea lol
To find out when the three trains will arrive at the station together again, we need to find the least common multiple (LCM) of their intervals. The intervals are 10 minutes, 12 minutes, and 15 minutes.
First, let's find the LCM of 10 and 12:
Multiples of 10: 10, 20, 30, 40, 50, 60, ...
Multiples of 12: 12, 24, 36, 48, 60, ...
The least common multiple of 10 and 12 is 60.
Now, let's find the LCM of 60 and 15:
Multiples of 60: 60, 120, 180, 240, ...
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
The least common multiple of 60 and 15 is 60.
Therefore, the three trains will arrive together at the station every 60 minutes.