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# 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?

Ravi is taking less time than Sonia in completing one round. Since they are going in the same direction they will surely meet again but at that time Ravi will have completed one round with respect to Sonia.

To find the minutes after which Ravi and Sonia will meet again we have to find 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.

$$18 = 2 × 3 × 3$$
$$12 = 2 × 2 × 3$$

LCM of 12 and 18 = $$2 × 2 × 3 × 3 =36$$

So, Ravi and Sonia will meet again at the starting point after 36 minutes.