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Four bells are arranged in such a manner that they ring once every 5,8,10 and 12 respectively. After how many minutes of their ringing simultaneously will

they ring again together.


See if we have to find when will they ring commonly we will have to find their lcm
and lcm of 5 8 10 12 is 120
means the the first will ring after 24 times
2nd - 15 times
3 - 12 times
4 - 10 times

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We find the LCM of 5,8, 10 & 12
We get,
The L.C.M as 120

Which means the bells will again ring after 120 minutes or 2 hours ( \frac{120}{60} )
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