Question
Download Solution PDFSeven bells ring at intervals of 2, 3, 4, 6, 8, 9 and 12 minutes, respectively. They started ringing simultaneously at 7.10 in the morning. What will be the next time when they all ring simultaneously?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Seven bells ring at intervals of 2, 3, 4, 6, 8, 9, and 12 minutes, respectively.
They started ringing simultaneously at 7:10 a.m.
Formula Used:
The time when all bells ring simultaneously is given by the Least Common Multiple (LCM) of their intervals.
Calculation:
Find the LCM of the intervals: 2, 3, 4, 6, 8, 9, and 12.
Prime factorization:
2 = 2
3 = 3
4 = 22
6 = 2 × 3
8 = 23
9 = 32
12 = 22 × 3
LCM = 23 × 32 = 8 × 9 = 72 minutes
Total time = 7:10 a.m. + 72 minutes
72 minutes = 1 hour 12 minutes
⇒ Next simultaneous ringing time = 7:10 a.m. + 1 hour 12 minutes
⇒ 8:22 a.m.
The next time when all the bells ring simultaneously is 8:22 a.m.
Last updated on Jun 2, 2025
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