If ratio and H.C.F. of two numbers are x : y and z. Find their L.C.M?

Options

A. `yz`
B. `(xz)/(y)`
C. `(xy)/(z)`
D. `xyz`

Answer

To find the L.C.M. of two numbers given their ratio and H.C.F., we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The ratio of the two numbers is given as \( x : y \).
- The H.C.F. (Highest Common Factor) of the two numbers is given as \( z \).

2. **Express the Two Numbers:**
- Since the ratio of the two numbers is \( x : y \), we can express the first number as:
\[ \text{First Number} = z \cdot x \]
- Similarly, the second number can be expressed as:
\[ \text{Second Number} = z \cdot y \]

3. **Calculate the L.C.M.:**
- The formula for finding the L.C.M. of two numbers when their H.C.F. is known is:
\[ \text{L.C.M.} = \frac{\text{First Number} \times \text{Second Number}}{\text{H.C.F.}} \]
- Substituting the values we have:
\[ \text{L.C.M.} = \frac{(z \cdot x) \times (z \cdot y)}{z} \]
- Simplifying this expression:
\[ \text{L.C.M.} = \frac{z^2 \cdot x \cdot y}{z} = z \cdot x \cdot y \]

4. **Final Result:**
- Therefore, the L.C.M. of the two numbers is:
\[ \text{L.C.M.} = z \cdot x \cdot y \]

### Summary:
The L.C.M. of the two numbers, given their ratio \( x : y \) and H.C.F. \( z \), is \( z \cdot x \cdot y \).

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