A and B start walking together from a point. Their steps measure 72 cm and 84 cm respectively. What is the minimum distance they should walk so that each takes exact number of steps?

Options

A. 2.7 m
B. 3.54 m
C. 6.3 m
D. 5.04 m

Answer

To solve the problem of finding the minimum distance A and B should walk so that each takes an exact number of steps, we need to follow these steps:

### Step 1: Identify the step lengths
- A's step length = 72 cm
- B's step length = 84 cm

### Step 2: Find the Least Common Multiple (LCM)
To ensure both A and B take an exact number of steps, we need to find the LCM of their step lengths (72 cm and 84 cm).

### Step 3: Prime Factorization
- Prime factorization of 72:
- 72 = 2 × 36
- 36 = 2 × 18
- 18 = 2 × 9
- 9 = 3 × 3
- Therefore, 72 = 2^3 × 3^2

- Prime factorization of 84:
- 84 = 2 × 42
- 42 = 2 × 21
- 21 = 3 × 7
- Therefore, 84 = 2^2 × 3^1 × 7^1

### Step 4: Calculate the LCM
To find the LCM, take the highest power of each prime factor:
- For 2: max(3, 2) = 3 → 2^3
- For 3: max(2, 1) = 2 → 3^2
- For 7: max(0, 1) = 1 → 7^1

Now, LCM = 2^3 × 3^2 × 7^1
- LCM = 8 × 9 × 7
- LCM = 72 × 7 = 504 cm

### Step 5: Convert to meters
Since the question asks for the distance in meters:
- 1 meter = 100 cm
- Therefore, to convert 504 cm to meters:
- Distance in meters = 504 cm / 100 = 5.04 meters

### Final Answer
The minimum distance they should walk so that each takes an exact number of steps is **5.04 meters**.

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