Six bells commence tolling together and toll at the intervals of 2,4,6,8,10,12…
2023
Six bells commence tolling together and toll at the intervals of 2,4,6,8,10,12 seconds respectively. In 60 minutes how many times they will toll together?
- A.
16
- B.
15
- C.
31
- D.
30
Attempted by 61 students.
Show answer & explanation
Correct answer: C
Solution:
Find the least common multiple (LCM) of the intervals 2, 4, 6, 8, 10, 12.
Prime factors give: 2 = 2, 4 = 2^2, 6 = 2·3, 8 = 2^3, 10 = 2·5, 12 = 2^2·3. Take highest powers: 2^3·3·5 = 8·3·5 = 120 seconds.
They therefore toll together every 120 seconds, i.e. every 2 minutes.
Total time = 60 minutes = 3600 seconds. Number of occurrences in 3600 seconds = 3600 / 120 = 30.
Conclusion: 30 times.
Note: If you include the initial simultaneous toll at time zero, there would be 31 times (including t = 0). The answer given here (30) counts the times after the commencement within the 60 minutes.