#### Question 7: There is a circular path around a sports field. Sonia takes 18 minutes to drive one round of the field, while Ravi take 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?

#### Explanatory Answer

Sonia takes 18 minutes to drive one round. So, Sonia will reach the starting point again after 18 minutes.

Infact, Sonia will be at the starting point every 18 minutes.

i.e., at time intervals that are multiple of 18.

Ravi takes 12 minutes to drive one round. So, Ravi will be at the starting point at time intervals that are multiples of 12.

Because they start at the same point at the same time they will meet again at the starting point at a time that is a multiple of 18 and 12.

The least such value is the least common multiple (LCM) of 18 and 12.

##### Compute LCM of 18 and 12

Step 1: Prime factorize the 2 numbers

18 = 2 × 3^{2}

12 = 2^{2} × 3

Step 2: **Compute LCM**: LCM = Product of the highest powers of all the primes in the 2 numbers.

LCM (18, 12) = 2^{2} × 3^{2} = 36

They will meet again at the starting point after 36 minutes.