Given that HCF (135,225)=45 find the LCM (135,225)

Answer

To find the LCM of the numbers 135 and 225 given that their HCF is 45, we can use the relationship between HCF and LCM. The formula is:

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

Where:
- \( a = 135 \)
- \( b = 225 \)
- \(\text{HCF}(135, 225) = 45\)

### Step-by-Step Solution:

1. **Write down the formula:**
\[ \text{HCF}(135, 225) \times \text{LCM}(135, 225) = 135 \times 225 \]

2. **Substitute the known values:**
\[ 45 \times \text{LCM}(135, 225) = 135 \times 225 \]

3. **Calculate the product \( 135 \times 225 \):**
- First, calculate \( 135 \times 225 \):
\[ 135 \times 225 = 30375 \]

4. **Now, substitute back into the equation:**
\[ 45 \times \text{LCM}(135, 225) = 30375 \]

5. **Solve for LCM:**
\[ \text{LCM}(135, 225) = \frac{30375}{45} \]

6. **Perform the division:**
- Calculate \( \frac{30375}{45} \):
\[ \text{LCM}(135, 225) = 675 \]

### Final Answer:
\[ \text{LCM}(135, 225) = 675 \]