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Question

A circular field  ha s 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.


Solution

Cyclist 1: Covers the entire circumference of field in 360/48 = 7.5 days = 180 hours

Cyclist 2: Covers the entire circumference of field in 360/60 = 6 days = 144 hours

Cyclist 3: Covers the entire circumference of field in 360/72 = 5 days = 120 hours

LCM of 180, 144, 120 gives when they would meet LCM = 720 hours = 720/ 24 = 30 day
First we will get how much time all three cyclist take to cover a circumference of 360 km. 
  So time taken for cyclist1 =360/48 = 7.5 days 
 
timet taken for cyclist2 = 360/60 = 6 days 
 
time taken for cyclist3 = 360/ 72 = 5 days 
 
  Here we can see 7.5, 6 , 5 is in l .c, m so we have to get l.c.m of 7.5, 6, 5 i.e 30 
so they will meet after 30 days. 
 
  in 30 days first cyclist will travel = 30/7.5= 4 rounds 
 
in 30 days 2nd cyclist will travel = 30/6= 5 rounds 
 
in 30 days third cyclist will travel = 30/5 = 6 rounds 
 
so after 30 days all the three cyclists will meet at start point
 

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