Question

There is a circular path around a sports field. Priya takes 18 minutes to drive one round of the field, while Ravish takes 12 minutes for the same. Suppose they both start at the same point and at the same time, and go in the same direction. After how many minutes will they meet again at the starting point?

Answer 1

Hint: For the solution of this question, we need to find the L.C.M. of 12 and 18.
L.C.M. stands for ‘Least Common Multiple’.The least common multiple of two numbers is the “smallest non-zero common number” which is a multiple of both the numbers.

Complete Step-by-step answer:

Time taken by Priya to drive one round of the circular path = 18 minutes

Time taken by Ravish to drive one round of the circular path = 12 minutes

Time after which they will meet again at the starting point = L.C.M. of 18 and 12

   = \[2\text{ }\times \text{ }2\text{ }\times \text{ }3\text{ }\times \text{ }3\] = 36

So, Priya and Ravish will meet again at the starting point after 36 minutes.

Note: One needs to be quite careful while obtaining the L.C.M. of the given numbers.
The L.C.M., that is the least common multiple or lowest common multiple or smallest common multiple of two integers a and b, is the smallest positive integer that is divisible by both a and b. In other words, we can say that L.C.M. of a number is the smallest positive number that is a multiple of two or more than two numbers.
For example, the L.C.M. ( Least Common Multiple ) of 3 and 5 is 15, because it is the smallest number that is completely divisible by 3 as well as 5.
3 and 5 do have other common multiples too, such as 30, 45, etc. but they all are larger than 15.