Three different clocks start chime together.then they chime at intervals 12,18 and 20 minutes respectively. When will they chime next time altogether? Write step by step procedure.


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Oddman answered
The clocks chime together at the least common multiple (LCM) of their chiming intervals. There are many ways to compute the LCM. One way looks at the factors of the numbers.
  12 = 2*2*3
  18 = 2*3*3
  20 = 2*2*5

The LCM will have the factors of all these numbers. It must have each factor repeated as many times as the number where that factor is most-repeated.
  2 is repeated 2 times in 12 and 20
  3 is repeated 2 times in 18
  5 is repeated 1 time in 20

LCM = 2*2*3*3*5 = 180

The clocks will chime together every 180 minutes, that is, every 3 hours. They will next chime together 3 hours after the last time they chimed together.

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