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Five bells begin to toll together and toll again at intervals of 6, 5, 7, 10 and 12 seconds respectively. How many times will they toll together in one hour excluding the one at the start?
The bells toll together every $$\text{LCM}(6, 5, 7, 10, 12) = 420$$ seconds. One hour has 3600 seconds, and $$\frac{3600}{420} \approx 8.57$$. So they toll together 8 times after the start.
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