During a morning walk, Akriti, Priya and Rinki step off together. Their steps measure 50 cm, 65 cm and 75 cm respectively. What is the minimum distance each should walk so that all can cover the same distance in complete steps ?

Options

A. 1595 cm
B. 1955 cm
C. 1185 cm
D. 1950 cm

Answer

To find the minimum distance that Akriti, Priya, and Rinki should walk so that all can cover the same distance in complete steps, we need to calculate the Least Common Multiple (LCM) of their step lengths: 50 cm, 65 cm, and 75 cm.

### Step-by-Step Solution:

1. **Identify the step lengths**:
- Akriti's step = 50 cm
- Priya's step = 65 cm
- Rinki's step = 75 cm

2. **Find the prime factorization of each step length**:
- For 50:
- 50 = 2 × 5²
- For 65:
- 65 = 5 × 13
- For 75:
- 75 = 3 × 5²

3. **List the prime factors**:
- From the factorizations, we have:
- 50: \(2^1\), \(5^2\)
- 65: \(5^1\), \(13^1\)
- 75: \(3^1\), \(5^2\)

4. **Identify the highest power of each prime factor**:
- The highest power of 2 is \(2^1\) (from 50).
- The highest power of 3 is \(3^1\) (from 75).
- The highest power of 5 is \(5^2\) (from both 50 and 75).
- The highest power of 13 is \(13^1\) (from 65).

5. **Calculate the LCM**:
- LCM = \(2^1 \times 3^1 \times 5^2 \times 13^1\)
- LCM = \(2 \times 3 \times 25 \times 13\)

6. **Perform the calculations**:
- First, calculate \(2 \times 3 = 6\).
- Then, calculate \(6 \times 25 = 150\).
- Finally, calculate \(150 \times 13 = 1950\).

7. **Conclusion**:
- The minimum distance each should walk so that all can cover the same distance in complete steps is **1950 cm**.