Miloni, Shikka and Varun start running around a circular stadium and complete one round in 8 seconds, 10 seconds and 14 seconds respectively. In how much time will they meet again at the starting point ?

Options

A. 3 minutes 12 seconds
B. 5 minutes 28 seconds
C. 2 minutes 45 seconds
D. 4 minutes 40 seconds

Answer

To find out when Miloni, Shikka, and Varun will meet again at the starting point after starting their runs around the circular stadium, we need to calculate the least common multiple (LCM) of the times they take to complete one round.

### Step-by-Step Solution:

1. **Identify the time taken by each runner:**
- Miloni completes one round in 8 seconds.
- Shikka completes one round in 10 seconds.
- Varun completes one round in 14 seconds.

2. **List the times:**
- Time for Miloni (M) = 8 seconds
- Time for Shikka (S) = 10 seconds
- Time for Varun (V) = 14 seconds

3. **Find the LCM of the three times (8, 10, and 14):**
- First, we find the prime factorization of each number:
- 8 = 2^3
- 10 = 2^1 × 5^1
- 14 = 2^1 × 7^1

4. **Determine the highest power of each prime number:**
- For the prime number 2, the highest power is 2^3 (from 8).
- For the prime number 5, the highest power is 5^1 (from 10).
- For the prime number 7, the highest power is 7^1 (from 14).

5. **Calculate the LCM:**
- LCM = 2^3 × 5^1 × 7^1
- LCM = 8 × 5 × 7
- LCM = 40 × 7
- LCM = 280 seconds

6. **Convert seconds into minutes and seconds:**
- 280 seconds can be converted to minutes by dividing by 60.
- 280 ÷ 60 = 4 minutes and 40 seconds (since 280 = 4 × 60 + 40).

### Final Answer:
Miloni, Shikka, and Varun will meet again at the starting point after **4 minutes and 40 seconds**.