A circular field has a circumference of 360 km. Three . . .

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

Doubt by Vikrant

Solution : 

Circumference of circle = 360 km

Time Taken by the first cyclist to complete the circular field = 360/48 = 7.5 days
Time Taken by the second cyclist to complete the circular field = 360/60 = 6 days

Time Taken by the third cyclist to complete the circular field = 360/72 = 5 days

Time after which they will meet again will be given by the LCM of 7.5, 6 and 5.

Now, you must be wondering, how to find the LCM of decimal number then here is the trick.

We need to multiply all three numbers with a common number such that the decimal should no longer be there. This is why we are multiplying each and every number with 10.

7.5, 6 and 5

75, 60 and 50

75=3×5²
60=2²×3×5

50=2×5²

LCM=2²×3×5²
LCM=4×3×25
LCM=12×25

LCM=300

Since, we have multiplied all the terms by 10, now we have to divide the final answer with 10 too. So the correct LCM is 300/10 = 30.

Hence, all the cyclist will meet again after 30 days.