Four friends step off together from the same spot . Their steps measure 18 cm , 36 cm , 45 cm and 72 cm respectively .What is the minimum distance in complete steps ?

Options

A. 280 cm
B. 340 cm
C. 360 cm
D. 420 cm

Answer

To find the minimum distance in complete steps that the four friends can walk together, we need to calculate the Least Common Multiple (LCM) of their step lengths: 18 cm, 36 cm, 45 cm, and 72 cm.

### Step-by-Step Solution:

1. **List the step lengths**:
- Friend 1: 18 cm
- Friend 2: 36 cm
- Friend 3: 45 cm
- Friend 4: 72 cm

2. **Find the prime factorization of each step length**:
- 18 = 2 × 3²
- 36 = 2² × 3²
- 45 = 3² × 5
- 72 = 2³ × 3²

3. **Identify the highest power of each prime factor**:
- For the prime factor 2: The highest power is 2³ (from 72).
- For the prime factor 3: The highest power is 3² (common in all).
- For the prime factor 5: The highest power is 5¹ (from 45).

4. **Multiply the highest powers of all prime factors together**:
- LCM = 2³ × 3² × 5¹
- Calculate each part:
- 2³ = 8
- 3² = 9
- 5¹ = 5

5. **Now multiply these results**:
- LCM = 8 × 9 × 5
- First, calculate 8 × 9 = 72
- Then, calculate 72 × 5 = 360

6. **Conclusion**:
- The minimum distance in complete steps that all four friends can walk together is **360 cm**.

### Final Answer:
The minimum distance in complete steps is **360 cm**.