If H.C.F. of 13 and 225 is 45, then their L.C.M. is :

Options

A. 405
B. 1125
C. 65
D. None of these

Answer

To find the LCM (Least Common Multiple) of two numbers when we know their HCF (Highest Common Factor), we can use the relationship between HCF and LCM, which is given by the formula:

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

Let's denote:
- HCF = 45
- LCM = ?
- First number = 13
- Second number = 225

### Step 1: Calculate the product of the two numbers
First, we need to calculate the product of the two numbers:

\[ \text{Product} = 13 \times 225 \]

Calculating this:

\[ 13 \times 225 = 2925 \]

### Step 2: Use the HCF and the product to find the LCM
Now, we can use the relationship between HCF and LCM:

\[ \text{HCF} \times \text{LCM} = \text{Product} \]

Substituting the known values:

\[ 45 \times \text{LCM} = 2925 \]

### Step 3: Solve for LCM
Now, we can solve for LCM:

\[ \text{LCM} = \frac{2925}{45} \]

Calculating this:

\[ \text{LCM} = 65 \]

### Final Answer
Thus, the LCM of 13 and 225 is **65**.

---