Question:

Given:
- Time taken by Sonia to complete one round = $18$ minutes.
- Time taken by Ravi to complete one round = $12$ minutes.
- Both start together from the same point and move in the same direction.

To Find: Time after which they will meet again at the starting point.

Step 1: Write the prime factorisation of the two times.
$$\begin{aligned}
18 &= 2 \times 3^2,\\
12 &= 2^2 \times 3.
\end{aligned}$$

Step 2: Determine the Least Common Multiple (LCM) using the highest powers of all prime factors.
$$\text{LCM}=2^2 \times 3^2 = 4 \times 9 = 36\text{ minutes}.$$

Step 3: Interpret the result.
- After $36$ minutes, Sonia will have completed $\dfrac{36}{18}=2$ rounds.
- After $36$ minutes, Ravi will have completed $\dfrac{36}{12}=3$ rounds.
Both have returned to the starting point simultaneously.

Conclusion: The two will meet again at the starting point after $36$ minutes.