A bell rings every 5 seconds. A second bell rings every 6 seconds and a third one rings every 8 seconds. If all the three rings at the same time at 8.00 a. m., at what time will they all ring together next?

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1 minute past 8.00 a . m .

2 minute past 8.00 a . m .

3 minute past 8.00 a . m .

4 minute past 8.00 a . m .

answer is B.

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Detailed Solution

The next time all three bells would ring simultaneously is at the LCM of 5 sec, 6 sec, and 8 sec.
The factors of 5, 6 and 8,

5 = 5

6 = 2 \times 3

8 = 2 \times 2 \times 2

So, the lowest common multiple (LCM) of 5, 6 and 8,

LCM (5, 6, 8) = 5 \times 3 \times 2 \times 2 \times 2

LCM (5, 6, 8) = 120

The LCM of 5, 6, 8 is 120 sec.
Now,
120 sec = 2 minutes. (since, 1 minute = 60 seconds)
So, they will therefore ring together again at 8:02 am or

2 minute past 8.00 a . m

Thus, the correct option is 2.

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