Calculate the product of LCM and HCF of 4 and 18.

Options

A. 72
B. 80
C. 82
D. 66

Answer

To solve the problem of calculating the product of the LCM (Least Common Multiple) and HCF (Highest Common Factor) of the numbers 4 and 18, we can follow these steps:

### Step 1: Identify the two numbers
Let \( x = 4 \) and \( y = 18 \).

### Step 2: Use the relationship between LCM and HCF
There is a useful formula that relates the product of two numbers to their LCM and HCF:
\[ \text{LCM}(x, y) \times \text{HCF}(x, y) = x \times y \]
This means that the product of the LCM and HCF of two numbers is equal to the product of the numbers themselves.

### Step 3: Calculate the product of the two numbers
Now, we can calculate the product of \( x \) and \( y \):
\[ x \times y = 4 \times 18 \]
Calculating this gives:
\[ 4 \times 18 = 72 \]

### Step 4: Conclusion
Thus, the product of the LCM and HCF of 4 and 18 is:
\[ \text{LCM}(4, 18) \times \text{HCF}(4, 18) = 72 \]

### Final Answer
The product of the LCM and HCF of 4 and 18 is **72**.

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