If the HCF of (336,54)=6, find the LCM (336,54)

Answer

To find the LCM of the numbers 336 and 54 given that their HCF is 6, we can use the relationship between HCF and LCM. The formula states:

\[ \text{HCF}(a, b) \times \text{LCM}(a, b) = a \times b \]

Where:
- \( a = 336 \)
- \( b = 54 \)
- \(\text{HCF}(336, 54) = 6\)

### Step-by-step Solution:

1. **Identify the numbers and their HCF**:
- We have \( a = 336 \) and \( b = 54 \).
- Given \( \text{HCF}(336, 54) = 6 \).

2. **Use the formula to express LCM**:
- Rearranging the formula gives us:
\[ \text{LCM}(a, b) = \frac{a \times b}{\text{HCF}(a, b)} \]

3. **Substitute the values into the formula**:
- Substitute \( a \), \( b \), and HCF into the equation:
\[ \text{LCM}(336, 54) = \frac{336 \times 54}{6} \]

4. **Calculate the product \( a \times b \)**:
- First, calculate \( 336 \times 54 \):
\[ 336 \times 54 = 18144 \]

5. **Divide by the HCF**:
- Now divide the product by the HCF:
\[ \text{LCM}(336, 54) = \frac{18144}{6} = 3024 \]

6. **Final Answer**:
- Therefore, the LCM of 336 and 54 is:
\[ \text{LCM}(336, 54) = 3024 \]