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There are two bells in the school. Bell A rings every 4 minutes. Bell B rings every 7 minutes. If both bells ring together at 10.04 p.m., when will they ring together again?

Question

There are two bells in the school. Bell A rings every 4 minutes. Bell B rings every 7 minutes. If both bells ring together at 10.04 p.m., when will they ring together again?

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Solution

To determine when both bells will ring together again, we need to find the least common multiple (LCM) of the two time intervals.

  1. Bell A rings every 4 minutes.
  2. Bell B rings every 7 minutes.

First, we find the prime factors of each number:

  • 4 = 2^2
  • 7 = 7 (7 is a prime number)

The LCM is found by taking the highest power of each prime number that appears in the factorization of either number:

  • The highest power of 2 is 2^2.
  • The highest power of 7 is 7.

Therefore, the LCM of 4 and 7 is: LCM=22×7=4×7=28 \text{LCM} = 2^2 \times 7 = 4 \times 7 = 28

So, the bells will ring together every 28 minutes.

If both bells ring together at 10:04 p.m., we add 28 minutes to this time: 10:04 p.m. + 28 minutes = 10:32 p.m.

Thus, the bells will ring together again at 10:32 p.m.

This problem has been solved

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