If H.C.F. of two numbers is 15 and their product is 1575, then their L.C.M. is

Options

A. 15
B. 105
C. 525
D. 1575

Answer

To solve the problem step by step, we will use the relationship between HCF (Highest Common Factor), LCM (Lowest Common Multiple), and the product of two numbers.

### Step-by-Step Solution:

1. **Understand the Given Information:**
- HCF of two numbers (let's call them A and B) is given as 15.
- The product of the two numbers (A × B) is given as 1575.

2. **Use the Relationship Between HCF, LCM, and Product:**
- There is a mathematical property that states:
\[ \text{HCF}(A, B) \times \text{LCM}(A, B) = A \times B \]
- We can rearrange this formula to find LCM:
\[ \text{LCM}(A, B) = \frac{A \times B}{\text{HCF}(A, B)} \]

3. **Substitute the Known Values:**
- We know:
- HCF(A, B) = 15
- A × B = 1575
- Substitute these values into the rearranged formula:
\[ \text{LCM}(A, B) = \frac{1575}{15} \]

4. **Perform the Division:**
- Now, calculate:
\[ \text{LCM}(A, B) = \frac{1575}{15} = 105 \]

5. **Conclusion:**
- Therefore, the LCM of the two numbers is **105**.

### Final Answer:
The LCM of the two numbers is **105**.

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