The HCF of two numbers is 15 and their LCM is 225. If one of the numbers is 75, then find the another number.

Options

A. 105
B. 90
C. 60
D. 45

Answer

To find the other number when the HCF and LCM are given, we can use the relationship between the two numbers, their HCF, and their LCM. The formula we will use is:

\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

Given:
- HCF = 15
- LCM = 225
- First Number = 75

We need to find the Second Number (let's denote it as \( x \)).

### Step-by-Step Solution:

1. **Write down the formula**:
\[ \text{HCF} \times \text{LCM} = \text{First Number} \times \text{Second Number} \]

2. **Substitute the known values into the formula**:
\[ 15 \times 225 = 75 \times x \]

3. **Calculate the left side**:
\[ 15 \times 225 = 3375 \]

4. **Set up the equation**:
\[ 3375 = 75 \times x \]

5. **Solve for \( x \)**:
\[ x = \frac{3375}{75} \]

6. **Calculate \( x \)**:
\[ x = 45 \]

Thus, the other number is **45**.

### Final Answer:
The other number is **45**.