If HCF of p and q is x and q = xy , then the LCM of p and q is

Options

A. xy
B. py
C. qy
D. pq

Answer

To find the LCM of \( p \) and \( q \) given that the HCF of \( p \) and \( q \) is \( x \) and \( q = xy \), we can follow these steps:

### Step 1: Understand the relationship between HCF and LCM
We know that the relationship between the HCF and LCM of two numbers \( p \) and \( q \) is given by the formula:
\[ \text{HCF}(p, q) \times \text{LCM}(p, q) = p \times q \]

### Step 2: Substitute the known values
From the problem, we have:
- HCF of \( p \) and \( q \) is \( x \)
- \( q = xy \)

We can substitute these values into the formula:
\[ x \times \text{LCM}(p, q) = p \times (xy) \]

### Step 3: Rearrange the equation to find LCM
Now, we can rearrange the equation to solve for LCM:
\[ \text{LCM}(p, q) = \frac{p \times (xy)}{x} \]

### Step 4: Simplify the expression
We can simplify the expression by canceling \( x \):
\[ \text{LCM}(p, q) = p \times y \]

### Final Answer
Thus, the LCM of \( p \) and \( q \) is:
\[ \text{LCM}(p, q) = p \times y \]

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