Riya , Manasvi and Pintu start running around a circular stadium and complete one round in 24 seconds , 6 seconds and 14 seconds respectively . In how much time will they meet again at the starting point ?

Options

A. 1 min 32 seconds
B. 4 min 8 seconds
C. 3 min 25 seconds
D. 2 min 48 seconds

Explanation

To find out when Riya, Manasvi, and Pintu will meet again at the starting point after they start running around the circular stadium, we need to calculate the Least Common Multiple (LCM) of their individual times to complete one round.

### Step 1: Identify the times taken by each runner
- Riya takes 24 seconds to complete one round.
- Manasvi takes 6 seconds to complete one round.
- Pintu takes 14 seconds to complete one round.

### Step 2: Find the LCM of the times
To find the LCM of 24, 6, and 14, we can use the prime factorization method.

1. **Prime Factorization**:
- 24 = 2^3 × 3^1
- 6 = 2^1 × 3^1
- 14 = 2^1 × 7^1

2. **Take the highest power of each prime**:
- For 2: The highest power is 2^3 (from 24).
- For 3: The highest power is 3^1 (from both 24 and 6).
- For 7: The highest power is 7^1 (from 14).

3. **Calculate the LCM**:
\[ \text{LCM} = 2^3 × 3^1 × 7^1 = 8 × 3 × 7 \]
\[ = 24 × 7 = 168 \]

### Step 3: Conclusion
The time at which Riya, Manasvi, and Pintu will meet again at the starting point is **168 seconds**.

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