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Question

A circular field has a circumference 360 km. three cyclists start together and can cycle 48 , 60 and 72 km a day round the field when will they meet again.

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Solution

Cyclist 1: Covers the entire circumference of field in 36048 = 7.5 days = 180 hours

Cyclist 2: Covers the entire circumference of field in 36060 = 6 days = 144 hours

Cyclist 3: Covers the entire circumference of field in 36072 = 5 days = 120 hours

LCM of 180, 144, 120 gives when they would meet LCM = 720 hours = 72024 = 30 days

So after 30 days all the three cyclists will meet at start point.


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