The LCM of two numbers is `(x +y)` and their HCF is `p (x- y).` If one of the number is 'p' then the other number is

Options

A. `p (x)/(y)`
B. `x ^(2) - y ^(2)`
C. `pxy`
D. `( px + y)/ ( px - y)`

Answer

To solve the problem, we will use the relationship between the LCM (Least Common Multiple), HCF (Highest Common Factor), and the two numbers involved. The relationship states that:

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

Given:
- LCM of the two numbers = \(x + y\)
- HCF of the two numbers = \(p(x - y)\)
- One of the numbers = \(p\)

Let the other number be \(N\). According to the relationship, we can write:

\[ (x + y) \times (p(x - y)) = p \times N \]

Now, we can simplify this equation to find \(N\):

1. Substitute the known values into the equation:
\[ (x + y) \times (p(x - y)) = p \times N \]

2. Divide both sides by \(p\) (assuming \(p \neq 0\)):
\[ (x + y)(x - y) = N \]

3. Now, we can express \(N\):
\[ N = (x + y)(x - y) \]

Thus, the other number is:

\[ N = (x + y)(x - y) \]

### Summary of the Solution Steps:
1. Write the relationship between LCM, HCF, and the two numbers.
2. Substitute the given values into the equation.
3. Simplify the equation to find the other number.