Ravin and Sikha drive around a circular sports field. Ravi takes `16` minutes to take one round while sikha completes the round in `20` minutes. If both start at the same point at the same time and go in same direction, after how much time will they meet at the starting point ?

Options

A. `"50 minutes"`
B. `"70 minutes"`
C. `"60 minutes"`
D. `"80 minutes"`

Explanation

To find out after how much time Ravi and Shikha will meet at the starting point while driving around a circular sports field, we need to determine the least common multiple (LCM) of the time it takes each of them to complete one round.

### Step-by-Step Solution:

1. **Identify the time taken by each person:**
- Ravi takes 16 minutes to complete one round.
- Shikha takes 20 minutes to complete one round.

2. **Find the LCM of 16 and 20:**
- First, we will find the prime factorization of both numbers.
- For 16:
- \(16 = 2^4\)
- For 20:
- \(20 = 2^2 \times 5^1\)

3. **Determine the LCM using the highest powers of the prime factors:**
- The prime factors involved are 2 and 5.
- The highest power of 2 from both factorizations is \(2^4\).
- The highest power of 5 from both factorizations is \(5^1\).
- Therefore, the LCM is calculated as:
\[ \text{LCM} = 2^4 \times 5^1 = 16 \times 5 = 80 \]

4. **Conclusion:**
- The LCM of 16 and 20 is 80 minutes.
- Thus, Ravi and Shikha will meet at the starting point after **80 minutes**.