Gulshan , Shakti and Om start running around a circular stadium and complete one round in 14 sec , 8 sec and 15 sec respectively . In how much time will they meet again at the starting point ?

Options

A. 23 min
B. 14 min
C. 13 min
D. 21 min

Explanation

To find out when Gulshan, Shakti, and Om will meet again at the starting point after starting to run 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 times taken by each runner:**
- Gulshan takes 14 seconds to complete one round.
- Shakti takes 8 seconds to complete one round.
- Om takes 15 seconds to complete one round.

2. **List the times:**
- The times are 14 seconds, 8 seconds, and 15 seconds.

3. **Find the prime factorization of each time:**
- 14 = 2 × 7
- 8 = 2^3
- 15 = 3 × 5

4. **Identify the highest power of each prime factor:**
- For the prime number 2: the highest power is 2^3 (from 8).
- For the prime number 3: the highest power is 3^1 (from 15).
- For the prime number 5: the highest power is 5^1 (from 15).
- For the prime number 7: the highest power is 7^1 (from 14).

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

6. **Perform the multiplication:**
- First, calculate 8 × 3 = 24
- Then, calculate 24 × 5 = 120
- Finally, calculate 120 × 7 = 840

7. **Conclusion:**
- The LCM of 14, 8, and 15 is 840 seconds.

8. **Convert seconds to minutes:**
- To convert seconds into minutes, divide by 60.
- 840 seconds ÷ 60 = 14 minutes.

Thus, Gulshan, Shakti, and Om will meet again at the starting point in **14 minutes**.