Question

Four bells begin to toll together and then each one at intervals of 6s, 7s, 8s and 9s, respectively. The number of times they will toll together in the next 1 hour is which of the following:

(a) 7 times
(b) 8 times
(c) 6 times
(d) Never

Answer 1

The number of times four bells toll together in the next hour is determined by finding the LCM of their tolling intervals. Since the LCM is 504 seconds, and there are 3600 seconds in an hour, the bells will toll together 7 times, hence the correct answer is (a) 7 times.

Step-by-step explanation:

To determine the number of times four bells toll together in one hour, we need to calculate the least common multiple (LCM) of their tolling intervals: 6 seconds, 7 seconds, 8 seconds, and 9 seconds.

We find the LCM by breaking down each number into its prime factorization:

• 6 = 2 × 3
• 7 = 7
• 8 = 23
• 9 = 32

The LCM will be the highest power of each prime present in the factorizations:

LCM(6, 7, 8, 9) = 23 × 32 × 7 = 504 seconds

There are 3600 seconds in one hour. To find how often the bells toll together in one hour, we divide 3600 seconds by the LCM:

3600 seconds / 504 seconds = 7.14...

Since the bells cannot toll together a fraction of a time, they will toll together exactly 7 times within one hour.

Therefore, the correct answer is (a) 7 times.