50 bells B1 , B2 , B3 ,.......B50 start ringing together. The bells ring after every 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.....50 sec respectively.How many times do all bells from B4, B9, B16, .....B49 ring together in 1 day ?

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Solution

The correct option is A
0

Bells B4, B9, B16.... B49 will ring together at the LCM of 4, 9, 16, 25, 36 and 49. These are the squares of 2, 3, 4, 5, 6 and 7. The LCM of 2, 3, 4, 5, 6 and 7 is 420. Hence the LCM of their squares will be square of the LCM = 420 $\times$ 420 = 176400. The bells will ring together after 176400 seconds or 49 hours. Hence they will not even ring together on the day in question.

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