A milkman has 75 lt milk in one cane and 45 lt in another, The maximum capacity of container which can measure milk of either container exact number :

Options

A. 1 litre
B. 5 litre
C. 15 litre
D. 25 litre

Answer

To find the maximum capacity of a container that can measure the milk from both cans (75 liters and 45 liters) in exact numbers, we need to determine the Highest Common Factor (HCF) of the two quantities.

### Step-by-Step Solution:

1. **Identify the quantities**: We have two quantities of milk, 75 liters and 45 liters.

2. **Find the prime factorization of each quantity**:
- For 75:
- 75 = 3 × 5 × 5 = 3 × 5²
- For 45:
- 45 = 3 × 3 × 5 = 3² × 5

3. **Identify the common prime factors**:
- The common prime factors between 75 and 45 are 3 and 5.

4. **Determine the lowest power of each common factor**:
- For the factor 3: The lowest power is 3¹ (from 75).
- For the factor 5: The lowest power is 5¹ (from 45).

5. **Calculate the HCF**:
- HCF = 3¹ × 5¹ = 3 × 5 = 15.

6. **Conclusion**: The maximum capacity of the container that can measure the milk from either container in exact numbers is **15 liters**.