Question

There is a circular path around a sports field. Sonia takes $18$ minutes to drive one round of the field, while Ravi 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

It can be observed that Ravi takes lesser time than Sonia to complete $1$ round of the circular path.
As they are going in the same direction, they will meet again at the same time when Ravi will have completed $1$ round $5$ of that circular path with respect to Sonia.
And the total time taken for completing this $1$ round of circular path will be the LCM of time taken by Sonia and Ravi for completing $1$ round of circular path respectively i.e., LCM of $18$ minutes and $12$ minutes.
$8 = 2 × 3 × 3$
And, $12 = 2 × 2 × 3$
LCM of $12$ and $18 = 2 × 2 × 3 × 3 = 36$

Therefore, Ravi and Sonia will meet together at the starting point after $36$ minutes.