Four bells toll at 4,7,12 and 84seconds.The bell toll together at 5o'clock.When will they again toll together?
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They will toll together for a 'common multiple' of (4,7,12,84), which is the l.c.m of these numbers.
4== 2^2
7 == 7
12 = 2^2 * 3
84 = 12 * 7 = 2^2 * 3 * 7
l.c.m(4,7,12,84) = 2^2 * 3 * 7 = 84 s
84 s = 1 min 24 sec
Hence they will toll together 84 seconds after 5 o'clock or 5:01:24 hrs ( 1 min 24 sec past 5 o'clock)
28 mins = 28*60 = 1680 sec
84 sec== toll 1 time
1680 sec== X times
X = 20 times
Hence,
They toll together at 5:01:24 hrs
In 28 mins they toll (together) 20 times.
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