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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? - Mathematics

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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?

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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

Concept: Euclid’s Division Lemma
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