Six bells commence tolling together and toll at intervals of 3, 6, 9, 12, 15…
2024
Six bells commence tolling together and toll at intervals of 3, 6, 9, 12, 15 and 18 seconds respectively. In 60 minutes, how many times do they toll together ?
- A.
10
- B.
20
- C.
21
- D.
25
Attempted by 72 students.
Show answer & explanation
Correct answer: C
Answer: 21
Explanation:
Compute the LCM of the intervals.
Prime factorizations: 3 = 3; 6 = 2·3; 9 = 3²; 12 = 2²·3; 15 = 3·5; 18 = 2·3². Take the highest powers: 2², 3², and 5.
LCM = 2² · 3² · 5 = 4 · 9 · 5 = 180 seconds.
Convert to minutes: 180 seconds = 3 minutes.
Count how many times in 60 minutes: they coincide every 3 minutes starting at time 0. There are 60/3 = 20 intervals of 3 minutes within 60 minutes, and including the initial simultaneous toll gives 20 + 1 = 21 times.
Therefore, the bells toll together 21 times in 60 minutes.