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LCM of time intervals — synchronized bells: Count joint tolls in one hour (excluding the start). Five bells toll together initially, then at intervals of 6, 5, 7, 10 and 12 seconds respectively. How many additional times do they toll together within 1 hour (excluding the initial toll at t = 0)? Choose the correct count.

Difficulty: Easy

7 times
8 times
9 times
11 times

Correct Answer: 8 times

Explanation:

Concept/Approach
They toll together every LCM of the intervals.

Compute LCM
LCM(6, 5, 7, 10, 12) = 2^2 × 3 × 5 × 7 = 420 seconds = 7 minutes.

Occurrences in 1 hour
3600 / 420 = 8.571… ⇒ 8 full additional meetings within 60 minutes.Times: 7, 14, 21, 28, 35, 42, 49, 56 minutes.

Final Answer
8 times

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