Four bells begin to toll together and then each one at intervals of 6, 7, 8…
2023
Four bells begin to toll together and then each one at intervals of 6, 7, 8 and 9 seconds respectively. The number of times they will toll together in the next 2 hours is:
- A.
14
- B.
15
- C.
13
- D.
11
Attempted by 79 students.
Show answer & explanation
Correct answer: B
Answer: 15 times
Explanation:
Find the prime factors: 6 = 2 × 3, 7 = 7, 8 = 2^3, 9 = 3^2.
Take the highest powers of each prime: 2^3, 3^2, and 7. So LCM = 2^3 × 3^2 × 7 = 504 seconds.
In 2 hours there are 2 × 60 × 60 = 7200 seconds. Divide: 7200 / 504 = 14.285..., so there are 14 full intervals of 504 seconds after the start.
Include the initial simultaneous toll at time 0. Total times they toll together = 14 + 1 = 15.
Therefore, the bells toll together 15 times in the next 2 hours.