The HCF of two numbers is 145 and their LCM is 2175 . If one of the numbers is 725 , the other number is

Options

A. 290
B. 435
C. 5
D. none of these

Answer

To find the other number when the HCF and LCM are given along with one of the numbers, we can use the relationship between HCF, LCM, and the two numbers.

### Step-by-Step Solution:

1. **Understand the relationship**: The relationship between the HCF (Highest Common Factor), LCM (Lowest Common Multiple), and the two numbers can be expressed as:
\[ \text{HCF} \times \text{LCM} = \text{Number 1} \times \text{Number 2} \]

2. **Identify the given values**:
- HCF = 145
- LCM = 2175
- Number 1 = 725
- Number 2 = ?

3. **Set up the equation**: Using the formula:
\[ 145 \times 2175 = 725 \times \text{Number 2} \]

4. **Calculate the left side**:
\[ 145 \times 2175 = 315375 \]

5. **Set up the equation with the known number**:
\[ 315375 = 725 \times \text{Number 2} \]

6. **Solve for Number 2**: To find Number 2, divide both sides by 725:
\[ \text{Number 2} = \frac{315375}{725} \]

7. **Perform the division**:
\[ \text{Number 2} = 435 \]

### Final Answer:
The other number is **435**.