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There are two bells in the school. Bell A rings every 9 minutes. Bell B rings every 6 minutes. If both bells ring together at 10.10 a.m., when will they ring together again?

Question

There are two bells in the school. Bell A rings every 9 minutes. Bell B rings every 6 minutes. If both bells ring together at 10.10 a.m., when will they ring together again?

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Solution

To find out when the two bells will ring together again, we need to find the least common multiple (LCM) of the two time intervals (9 minutes and 6 minutes).

Step 1: List the multiples of each number Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, 81, 90... Multiples of 6: 6, 12, 18, 24, 30, 36, 42, 48, 54, 60...

Step 2: Find the least common multiple The least common multiple of 9 and 6 is 18.

This means that the two bells will ring together every 18 minutes.

Step 3: Add this interval to the initial time If they first rang together at 10:10 a.m., adding 18 minutes to this time gives 10:28 a.m.

So, the two bells will ring together again at 10:28 a.m.

This problem has been solved

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