Three person start walking from a same point. There steps are of 63 cm, 70 cm & 77 cm respectively. What is minimum distance which all three of them can cover in complete steps?

Options

A. 9630 cm
B. 9360 cm
C. 6930 cm
D. 6950 cm

Answer

To find the minimum distance that all three persons can cover in complete steps, we need to calculate the Least Common Multiple (LCM) of their step lengths: 63 cm, 70 cm, and 77 cm.

### Step-by-step Solution:

1. **Find the prime factorization of each step length:**
- For 63:
- \( 63 = 3^2 \times 7^1 \)
- For 70:
- \( 70 = 2^1 \times 5^1 \times 7^1 \)
- For 77:
- \( 77 = 7^1 \times 11^1 \)

2. **Identify the highest power of each prime factor:**
- From 63: \( 3^2 \)
- From 70: \( 2^1 \), \( 5^1 \), \( 7^1 \)
- From 77: \( 7^1 \), \( 11^1 \)

The highest powers are:
- \( 3^2 \) from 63
- \( 2^1 \) from 70
- \( 5^1 \) from 70
- \( 7^1 \) from both 70 and 77
- \( 11^1 \) from 77

3. **Multiply these highest powers together to find the LCM:**
\[ LCM = 3^2 \times 2^1 \times 5^1 \times 7^1 \times 11^1 \]

4. **Calculate the LCM:**
- First, calculate \( 3^2 = 9 \)
- Then multiply:
\[ 9 \times 2 = 18 \]
\[ 18 \times 5 = 90 \]
\[ 90 \times 7 = 630 \]
\[ 630 \times 11 = 6930 \]

5. **Conclusion:**
The minimum distance that all three persons can cover in complete steps is **6930 cm**.