Calculate the LCM of two positive. Integers whose product is 108 and HCF is 3.

Options

A. 72
B. 36
C. 18
D. 9

Answer

To calculate the LCM of two positive integers whose product is 108 and HCF is 3, we can follow these steps:

### Step 1: Understand the relationship between LCM, HCF, and the product of two numbers.
The relationship is given by the formula:
\[ \text{LCM} \times \text{HCF} = \text{Product of the two numbers} \]

### Step 2: Substitute the known values into the formula.
We know:
- Product of the two numbers = 108
- HCF = 3

Using the formula:
\[ \text{LCM} \times 3 = 108 \]

### Step 3: Solve for LCM.
To find LCM, we can rearrange the equation:
\[ \text{LCM} = \frac{\text{Product of the two numbers}}{\text{HCF}} = \frac{108}{3} \]

### Step 4: Perform the division.
Now, we calculate:
\[ \text{LCM} = \frac{108}{3} = 36 \]

### Conclusion:
The LCM of the two positive integers is 36.

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