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

Given: Circumference of field = 360 km

Distance covered by cyclist 1 = 48 km

Distance covered by cyclist 2 = 60 km

Distance covered by cyclist 3 = 72 km

To find: The time when they meet.

Explanation:

Circumference of the circular field is 36 km.
Use the formula:

So time taken by a cyclist = circumference of field / speed of cyclist

Time taken by first cyclist

= 7.5 days
As 1 day = 24 hours
⇒ 7.5×24 = 180 Hrs

Similarly,

Time taken by second cyclist

= 6 days
⇒ 6×24 = 144 Hrs

Time taken by third cyclist

= 5 days
⇒ 5×24 = 120
we need to find the minimum time at which they will meet.
So we need to find LCM of the time they all take.

Now LCM of 180, 144 and 120 is 720 hours,

Therefore, the time when all three will meet again

= 30 days
Note: To find the minimum of given values always find their L.C.M.