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25 August, 01:25

In a clock, a large gear completes a rotation every 45 seconds and a small gear completes a rotation every 18 seconds. How many seconds pass before the gears align again?

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  1. 25 August, 03:40
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    Essentially you want to know what the least common multiple of their respective rate times ...

    18=2*3*3 and 45=3*3*5 so the least common multiple is 2*3*3*5=90

    check

    90/45=2 rev

    90/18=5 rev

    Notice that these are complete revolutions which is what we want, complete revolutions at the same time ...
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