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Question
Six bells commence tolling together and toll at intervals of 2, 4, 6, 8, 10, 12 minutes respectively. In 30 hours, how many times do they toll together?
Solution
Six bells toll together at intervals of 2,4, 6, 8, 10 and 12 minutes, respectively.
Prime factorization:
2 = 2
4 = 2 × 2
6 = 2 × 3
8 = 2 × 2 × 2
10 = 2 × 5
12 = 2 × 2 × 3
∴ LCM (2, 4, 6, 8, 10, 12) = 23 × 3 × 5 = 120
Hence, after every 120minutes (i.e. 2 hours), they will toll together.
∴ Required number of times = `(30/2+1) `= 16
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