Three man step off together from the same spot. Their steps measure 63 cm, 70 cm, and 77 cm respectively . The minimum distance each should cover so that all can cover the distance in complate steps is

Options

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

Answer

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

### Step-by-Step Solution:

1. **Identify the step lengths**:
- Man A: 63 cm
- Man B: 70 cm
- Man C: 77 cm

2. **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:
- \( 77 = 7^1 \times 11^1 \)

3. **Determine the LCM**:
- The LCM is found by taking the highest power of each prime factor that appears in the factorizations.
- From the factorizations:
- The highest power of 2: \( 2^1 \) (from 70)
- The highest power of 3: \( 3^2 \) (from 63)
- The highest power of 5: \( 5^1 \) (from 70)
- The highest power of 7: \( 7^1 \) (common in all three)
- The highest power of 11: \( 11^1 \) (from 77)
- Therefore, the LCM is:
\[ LCM = 2^1 \times 3^2 \times 5^1 \times 7^1 \times 11^1 \]

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

5. **Conclusion**:
- The minimum distance that each man should cover so that all can cover the distance in complete steps is **6930 cm**.