Assertion (A): For any two positive numbers a and b, HCF`(a,b)xxLCM)(a,b)=axxb`.
Reason(R):The HCF of any two numbers is 5 and their products is 150. Then their LCM is 40.

Options

A. Both A and R are true and R is the correct explanation for A .
B. Both A and Rare true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the problem, we need to analyze the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
The assertion states that for any two positive numbers \( a \) and \( b \), the relationship \( \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \) holds true.
- This is a well-known property of HCF and LCM, and it is indeed true.

2. **Understanding the Reason (R)**:
The reason states that the HCF of two numbers is 15 and their product is 150, then their LCM is 40.
- We can use the relationship from the assertion to check if this is correct. According to the formula:
\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \]
- Given that \( \text{HCF}(a, b) = 15 \) and \( a \times b = 150 \), we can substitute these values into the formula:
\[ \text{LCM}(a, b) = \frac{150}{15} = 10 \]
- The reason states that the LCM is 40, which contradicts our calculation. Therefore, the reason is false.

3. **Conclusion**:
- The assertion (A) is true.
- The reason (R) is false.
- Thus, the correct conclusion is that the assertion is true, but the reason is false.

### Final Answer:
- Assertion (A) is true.
- Reason (R) is false.