If the HCF of two numbers is 2 and their LCM is 27, what is the product of the two numbers?

Options

A. 54
B. 27
C. 45
D. 82

Answer

To solve the problem, we can use the relationship between the Highest Common Factor (HCF), Lowest Common Multiple (LCM), and the product of two numbers. The relationship is given by the formula:

\[ \text{Product of two numbers} = \text{HCF} \times \text{LCM} \]

### Step-by-Step Solution:

1. **Identify the given values**:
- HCF of the two numbers = 2
- LCM of the two numbers = 27

2. **Use the formula**:
- According to the formula, we can express the product of the two numbers (let's call them A and B) as:
\[ A \times B = \text{HCF} \times \text{LCM} \]

3. **Substitute the known values into the formula**:
- Substitute the values of HCF and LCM into the equation:
\[ A \times B = 2 \times 27 \]

4. **Perform the multiplication**:
- Calculate the product:
\[ A \times B = 54 \]

5. **Conclusion**:
- The product of the two numbers is 54.

### Final Answer:
The product of the two numbers is **54**.

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