A train for Aurangabad leaves station every 7 minutes. Another train for Pune city leaves the station every 6 minutes. Suppose it's 6.30 a.m. right now. At what time will both trains leave the station together?

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Solution

A train leaves for Aurangabad station and Pune station every 7 minutes and 6 minutes respectively.
So both trains leaving the station together next will be at LCM of 7 and 6.
Multiple of 7 = 7, 14, 21, 28, 35, 42, 49, and so on.
Multiple of 6 = 6, 12, 18, 24, 30, 36, 42, 48 and so on.

LCM of 7 and 6 = 42.
The time both the trains last left together is at 6.30 a.m.
So, next time they will leave together will be:
6.30 a.m. + 42 minute = 7.12 a.m.

Therefore at 7.12 a.m., both trains will next leave the station together.

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