Three persons started together for their morning walk. Their steps measure 15 cm, 25 cm and 30 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps?

Answer

To find the minimum distance that each person should walk so that all can cover the same distance in complete steps, we need to determine the Lowest Common Multiple (LCM) of their step lengths: 15 cm, 25 cm, and 30 cm.

### Step-by-Step Solution:

1. **Identify the Step Lengths**:
- Person A's step length: 15 cm
- Person B's step length: 25 cm
- Person C's step length: 30 cm

2. **List the Step Lengths**:
- We have the numbers: 15, 25, and 30.

3. **Find the Prime Factorization**:
- For 15:
- \( 15 = 3 \times 5 \)
- For 25:
- \( 25 = 5 \times 5 = 5^2 \)
- For 30:
- \( 30 = 2 \times 3 \times 5 \)

4. **Identify the Highest Powers of Each Prime Factor**:
- The prime factors we have are 2, 3, and 5.
- The highest power of each prime factor from the factorizations:
- For 2: \( 2^1 \) (from 30)
- For 3: \( 3^1 \) (from 15 and 30)
- For 5: \( 5^2 \) (from 25)

5. **Calculate the LCM**:
- LCM = \( 2^1 \times 3^1 \times 5^2 \)
- Calculate:
- \( 2 \times 3 = 6 \)
- \( 5^2 = 25 \)
- \( 6 \times 25 = 150 \)

6. **Conclusion**:
- The minimum distance each person should walk so that all can cover the same distance in complete steps is **150 cm**.