The product of two numbers is 216. If the H.C.F is 6, then their L.C.M is:

Options

A. a. 72
B. b. 60
C. c. 48
D. d. 36

Answer

To find the LCM of two numbers given their product and HCF, we can use the relationship between HCF, LCM, and the product of the two numbers. Here’s the step-by-step solution:

### Step 1: Understand the relationship
We know that:
\[ \text{HCF} \times \text{LCM} = \text{Product of the two numbers} \]

### Step 2: Substitute the known values
From the question, we have:
- Product of the two numbers = 216
- HCF = 6

Substituting these values into the formula gives us:
\[ 6 \times \text{LCM} = 216 \]

### Step 3: Solve for LCM
To find the LCM, we can rearrange the equation:
\[ \text{LCM} = \frac{216}{6} \]

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

### Conclusion
Thus, the LCM of the two numbers is **36**.

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