Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and…
2024
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8 10 and 12 seconds respectively. In 30 minutes, how many times do they toll together?
- A.
24
- B.
21
- C.
15
- D.
16
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Show answer & explanation
Correct answer: D
Key insight: the bells all toll together at intervals equal to the least common multiple of their individual intervals.
Compute the LCM of 2, 4, 6, 8, 10 and 12:
LCM(2,4,6,8,10,12) = 120 seconds, i.e., every 2 minutes they toll together.
Total time = 30 minutes = 1800 seconds.
Number of coincidences after time 0 = 1800 ÷ 120 = 15.
Include the initial simultaneous toll at time 0: total = 15 + 1 = 16.
Answer: They toll together 16 times in 30 minutes.