If HCF (a,b) =45 and `a times b=30375` then LCM (a,b) is

Options

A. 1875
B. 1350
C. 625
D. 675

Answer

To solve the problem, we need to find the Least Common Multiple (LCM) of two numbers \(a\) and \(b\) given their Highest Common Factor (HCF) and the product of the two numbers.

### Step-by-Step Solution:

1. **Understand the relationship between HCF, LCM, and the product of two numbers**:
The relationship is given by the formula:
\[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \]
This means that the product of the HCF and LCM of two numbers is equal to the product of the numbers themselves.

2. **Substitute the known values into the formula**:
We know:
- \(\text{HCF}(a, b) = 45\)
- \(a \times b = 30375\)

Using the formula:
\[ 45 \times \text{LCM}(a, b) = 30375 \]

3. **Rearrange the formula to find LCM**:
To find \(\text{LCM}(a, b)\), we can rearrange the equation:
\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \]

4. **Substitute the values into the rearranged formula**:
Now substitute the known values:
\[ \text{LCM}(a, b) = \frac{30375}{45} \]

5. **Perform the division**:
Now, we need to calculate:
\[ \text{LCM}(a, b) = \frac{30375}{45} = 675 \]

6. **Conclusion**:
Therefore, the LCM of \(a\) and \(b\) is:
\[ \text{LCM}(a, b) = 675 \]

### Final Answer:
The LCM of \(a\) and \(b\) is **675**.