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7 bells ring at interval of 2, 3, 4, 6, 8, 9 and 12 seconds, respectively. They started ringing simultaneously. How many times will they ring together in 1 hour?

7 bells ring at interval of 2, 3, 4, 6, 8, 9 and 12 seconds, respectively. They started ringing simultaneously. How many times will they ring together in 1 hour? Correct Answer 51

GIVEN:

7 bells ring at interval of 2, 3, 4, 6, 8, 9 and 12 seconds, respectively.

CONCEPT:

Concept of LCM (Least common multiple): Least value which is exactly divisible by all the given numbers

CALCULATION:

The time periods of the bells are 2, 3, 4, 6, 8, 9 and 12 seconds.

⇒ They will ring together in LCM(2, 3, 4, 6, 8, 9, 12) seconds

⇒ 2 × 3 × 2 × 2 × 3 = 72 seconds = 1.2 minutes

∴ In 1 hour = 60 minutes they ring (60/1.2 + 1) = 51 times

Mistake Points

1 should be added in the end as all the bell rang together in the starting also.

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