If H.C.F. of 135 and 225 is 45, then find their L.C.M.

Answer

To find the L.C.M. of 135 and 225 given that their H.C.F. is 45, we can use the relationship between H.C.F., L.C.M., and the two numbers. The formula is:

\[ \text{H.C.F.} \times \text{L.C.M.} = \text{A} \times \text{B} \]

where A and B are the two numbers.

### Step-by-Step Solution:

1. **Identify the given values:**
- A = 135
- B = 225
- H.C.F. = 45

2. **Use the formula:**
\[ \text{H.C.F.} \times \text{L.C.M.} = A \times B \]
Plugging in the known values:
\[ 45 \times \text{L.C.M.} = 135 \times 225 \]

3. **Calculate \(135 \times 225\):**
- First, we can break it down:
\[ 135 \times 225 = 135 \times (200 + 25) = 135 \times 200 + 135 \times 25 \]
- Calculate \(135 \times 200\):
\[ 135 \times 200 = 27000 \]
- Calculate \(135 \times 25\):
\[ 135 \times 25 = 3375 \]
- Now add them together:
\[ 27000 + 3375 = 30375 \]

4. **Set up the equation to find L.C.M.:**
\[ 45 \times \text{L.C.M.} = 30375 \]

5. **Solve for L.C.M.:**
\[ \text{L.C.M.} = \frac{30375}{45} \]

6. **Perform the division:**
- To simplify \(30375 \div 45\):
\[ 30375 \div 45 = 675 \]

7. **Conclusion:**
- Therefore, the L.C.M. of 135 and 225 is \(675\).

### Final Answer:
\[ \text{L.C.M.} = 675 \]