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Mathematics

Three bells are ringing continuously at intervals of 30, 36 and 45 minutes respectively. At what time will they ring together again if they ring simultaneously at 8 a.m.?

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Answer

The required time interval is the LCM of 30, 36 and 45.

230, 36, 45
215, 18, 45
315, 9, 45
35, 3, 15
55, 1, 5
1, 1, 1

LCM of 30, 36 and 45 = 2 × 2 × 3 × 3 × 5 = 180 minutes.

Converting to hours: 180 minutes = 3 hours.

The bells ring simultaneously at 8 a.m. So they will ring together again at:

8 a.m. + 3 hours = 11 a.m.

Hence, the bells will ring together again at 11 a.m.

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