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 :

They will be again at the starting point at least common multiples of 18 and 12 minutes. To find the L.C.M of 18 and 12, we have :

18 = \(2 \times 3\times 3\)

and  12 = \(2 \times 2 \times 3\)

L.C.M of 18 and 12 = \(2 \times 2 \times 3 \times 3\) = 36

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