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 ?
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
To solve this problem, we first need to find the least common multiple (LCM) of the intervals at which the bells toll. The LCM of 2, 4, 6, 8, 10, and 12 is 120. This means that all six bells will toll together every 120 minutes, or every 2 hours.
Next, we need to determine how many 2-hour periods there are in 30 hours. To do this, we divide 30 by 2, which gives us 15. This means that the bells will toll together 15 times in 30 hours.
However, we must add 1 to this total because the bells also toll together at the start of the 30-hour period. Therefore, the bells toll together 16 times in 30 hours.
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