Limousines travelling from the downtown hotel to the airport follow different routes. Those servicing Route A leave every 60 minutes, Route B every 30 minutes and Route C every 45 minutes. If the first departure on each route is 6:30am, when will be the next time limousines depart at the same time on all three route?
Suppose it happens x minutes after. Then x has to be divisible by 30, 45 and 60. Since we are looking for the next time it happens x has to be the smallest possible. So we need to find a least common multiple of 30, 45 and 60. 30 = 15 × 2 45 = 15 × 3 60 = 15 × 4 Therefore least common multiple is 15 x 3 x 4 = 180. So in 180 minutes (3 hours) they will depart at the same time. 3 hours after 6:30 a.m. is 9:30 am.
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