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.

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?

Sonia takes $18$ minutes for one round, and Ravi takes $12$ minutes for one round.

Step 1: Find the prime factorization of $18$ and $12$:
$18=2\times 3^2$
$12=2^2\times 3$

Step 2: LCM is the product of all prime factors, each raised to the highest power:
$LCM(18,12)=2^2\times 3^2=36$

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

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