If the product of numbers is 1500 and their HCF is 10, then find the LCM.

Options

A. 15000
B. 150
C. 1500
D. 15

Answer

To solve the problem, we can use the relationship between the HCF (Highest Common Factor), LCM (Least Common Multiple), and the product of two numbers. The formula is:

\[ \text{HCF} \times \text{LCM} = \text{Product of the numbers} \]

Given:
- Product of the numbers = 1500
- HCF = 10

We need to find the LCM.

### Step-by-step Solution:

1. **Write down the formula**:
\[ \text{HCF} \times \text{LCM} = \text{Product of the numbers} \]

2. **Substitute the known values into the formula**:
\[ 10 \times \text{LCM} = 1500 \]

3. **Isolate LCM**:
To find LCM, divide both sides of the equation by 10:
\[ \text{LCM} = \frac{1500}{10} \]

4. **Calculate the LCM**:
\[ \text{LCM} = 150 \]

5. **Final Answer**:
The LCM of the numbers is **150**.