The LCM of two numbers is 30 and the product of two numbers is 150. Find the HCF

Options

A. 3
B. 5
C. 10
D. 15

Answer

To find the HCF (Highest Common Factor) of two numbers when given their LCM (Lowest Common Multiple) and the product of the two numbers, we can use the relationship between these three quantities.

**Step-by-step solution:**

1. **Understand the relationship**: The relationship between LCM, HCF, and the product of two numbers can be expressed as:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]

2. **Identify the given values**: From the question, we know:
- LCM = 30
- Product of the two numbers = 150

3. **Set up the equation**: Using the relationship mentioned above, we can substitute the known values into the equation:
\[ 30 \times \text{HCF} = 150 \]

4. **Solve for HCF**: To find the HCF, we can rearrange the equation:
\[ \text{HCF} = \frac{150}{30} \]

5. **Calculate the HCF**: Now, perform the division:
\[ \text{HCF} = 5 \]

6. **Final answer**: The HCF of the two numbers is 5.