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
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?

Solution:

LCM of $18 \& 12$

$18=2 \times 3^{2}$

$12=2^{2} \times 3$

$\operatorname{LCM}(18,12)=2^{2} \times 3^{2}=36$

Thus, after 36 minutes they will meet again at the starting point.
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