Haris , Dilip and Asha start running around a circular stadium and complete one round in 27 seconds , 9 seconds and 36 seconds respectively . In how many time will they meet again at the starting point ?

Options

A. 1 min 48 sec
B. 2 min 36 sec
C. 3 min 11 sec
D. 2 min 25 sec

Explanation

To find out when Haris, Dilip, and Asha will meet again at the starting point after they start running around a circular stadium, we need to determine the least common multiple (LCM) of their individual lap times.

### Step-by-Step Solution:

1. **Identify the lap times**:
- Haris completes one round in 27 seconds.
- Dilip completes one round in 9 seconds.
- Asha completes one round in 36 seconds.

2. **Find the prime factorization of each time**:
- For 27:
\[ 27 = 3^3 \]
- For 9:
\[ 9 = 3^2 \]
- For 36:
\[ 36 = 2^2 \times 3^2 \]

3. **Determine the LCM**:
- To find the LCM, take the highest power of each prime factor present in the factorizations:
- For the prime number 2: highest power is \(2^2\) (from 36).
- For the prime number 3: highest power is \(3^3\) (from 27).
- Therefore, the LCM is calculated as:
\[ LCM = 2^2 \times 3^3 = 4 \times 27 = 108 \]

4. **Convert LCM to minutes and seconds**:
- The LCM we found is 108 seconds.
- To convert seconds into minutes and seconds:
- Divide 108 by 60:
\[ 108 \div 60 = 1 \text{ minute and } 48 \text{ seconds} \]

5. **Final Answer**:
- Haris, Dilip, and Asha will meet again at the starting point after **1 minute and 48 seconds**.