If the L.C.M. of `x` and `y` is `z` , their H.C.F. is -

Options

A. `(xy)/z`
B. `xyz`
C. `(x+y)/z`
D. `z/(xy)`

Answer

To find the H.C.F. (Highest Common Factor) of two numbers \( x \) and \( y \) when their L.C.M. (Lowest Common Multiple) is given as \( z \), we can use the relationship between L.C.M., H.C.F., and the two numbers.

### Step-by-Step Solution:

1. **Understand the Relationship**:
The relationship between the two numbers, their L.C.M., and their H.C.F. is given by the formula:
\[ x \times y = \text{L.C.M.}(x, y) \times \text{H.C.F.}(x, y) \]

2. **Substitute the Given Values**:
According to the problem, the L.C.M. of \( x \) and \( y \) is \( z \). Therefore, we can substitute \( z \) into the formula:
\[ x \times y = z \times \text{H.C.F.}(x, y) \]

3. **Rearrange the Formula**:
To find the H.C.F., we need to isolate it. We can do this by dividing both sides of the equation by \( z \):
\[ \text{H.C.F.}(x, y) = \frac{x \times y}{z} \]

4. **Final Result**:
Thus, the H.C.F. of \( x \) and \( y \) is:
\[ \text{H.C.F.}(x, y) = \frac{x \times y}{z} \]