the HCF of two numbers is 6. If the numbers are 24 and 42, find their LCM.

Answer

To find the LCM (Least Common Multiple) of the numbers 24 and 42, given that their HCF (Highest Common Factor) is 6, we can use the relationship between LCM, HCF, and the two numbers. The formula we will use is:

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

### Step-by-step solution:

1. **Identify the given values**:
- HCF = 6
- First number = 24
- Second number = 42

2. **Calculate the product of the two numbers**:
\[ \text{Product} = 24 \times 42 \]
- First, calculate \( 24 \times 42 \):
- \( 24 \times 42 = 1008 \)

3. **Use the formula to find LCM**:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]
- Substitute the known values into the formula:
\[ \text{LCM} \times 6 = 1008 \]

4. **Solve for LCM**:
- To isolate LCM, divide both sides by 6:
\[ \text{LCM} = \frac{1008}{6} \]
- Calculate \( \frac{1008}{6} \):
- \( 1008 \div 6 = 168 \)

5. **Conclusion**:
- Therefore, the LCM of 24 and 42 is **168**.