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 $\frac{360}{48}$ = 7.5 days = 180 hours
Cyclist 2: Covers the entire circumference of field in $\frac{360}{60}$ = 6 days = 144 hours
Cyclist 3: Covers the entire circumference of field in $\frac{360}{72}$ = 5 days = 120 hours
LCM of 180, 144, 120 gives when they would meet LCM = 720 hours = $\frac{720}{24}$ = 30 days
So after 30 days all the three cyclists will meet at start point.

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