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+1 vote
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in Mathematics by (33.0k points)

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? 

1 Answer

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Best answer

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 120 minutes (i.e. 2 hours), they will toll together.

∴ Required number of times = (30/2 +1) = 16

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