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?

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#### Solution

Sincethey both move inthe same direction and at the same time, to find the time when will they both meet together again, it is enough if we find the LCM of 12 and 18

12 = 2^{2} x 3 x 1

18 = 3^{2} x 2 x 1

LCM (18, 12) = 2 x 3 x 3 x 2 x 1 = 36

Therefore Sonia and Ravi willmeet again after 36 minutes

Concept: Fundamental Theorem of Arithmetic

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