Three bells toll at intervals of 9, 12, and 15 minutes. If they start tolling together, after what time will they next toll together?

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1 hour

112

hour

212

hour

3 hours

answer is D.

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Detailed Solution

The given data is as follows.
Three bells toll at intervals of 9, 12, and 15 minutes.
We are required to find after how much time they will start tolling together again when they start tolling together.
We shall find the LCM of 48, 72, and 108; by dividing these numbers by least common multiples until no further division is possible and then multiplying all the divisors which are prime numbers.

3 9, 12, 15 3, 4, 5 ⇒ L C M = 32 × 4 × 5 = 180

The required time for tolling together again is

⇒ 180 minutes ⇒ 18060 hours ⇒ 3 hours

Therefore, the bells that toll at intervals of 9, 12, and 15 minutes; will start tolling together again after 3 hours.
Hence the correct answer is option (4).

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