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?

From the question, it is given that Ravi and Sonia start from the same point but take different time to complete the round. So, now we have to find the time taken by both of them to meet again at the starting point.

That means we have to find the LCM of 18 and 12.

Now we will find the LCM of 18 and 12 by prime factorization method:

18 = 2 × 3²

12 = 2² × 3

Now, prime factor 2 and 3 are common here. So, take prime factors with highest power i.e. 2² and 3².

L.C.M. = 2² × 3² = 4 × 9 = 36 minutes.

Hence, time taken by Ravi and Sonia to meet again at the starting point is 36 minutes.