If x : y be the ratio of two whole numbers and z be their HCF, then the LCM of those two number is :

Options

A. a) `yz`
B. b) `(xz)/y`
C. c) `(xy)/z`
D. d) `xyz`

Answer

To find the LCM of two whole numbers given their ratio and HCF, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have two whole numbers whose ratio is given as \( x : y \).
- The HCF (Highest Common Factor) of these two numbers is given as \( z \).

2. **Express the Whole Numbers**:
- Let the two whole numbers be \( a \) and \( b \).
- Based on the ratio \( x : y \), we can express the numbers as:
\[ a = kx \quad \text{and} \quad b = ky \]
where \( k \) is a common multiplier.

3. **Use the Relationship Between HCF and LCM**:
- The relationship between HCF and LCM of two numbers is given by:
\[ \text{LCM}(a, b) \times \text{HCF}(a, b) = a \times b \]
- Substituting the expressions for \( a \) and \( b \):
\[ \text{LCM}(kx, ky) \times z = (kx) \times (ky) \]

4. **Simplify the Equation**:
- The right-hand side simplifies to:
\[ k^2xy \]
- Therefore, we have:
\[ \text{LCM}(kx, ky) \times z = k^2xy \]

5. **Solve for LCM**:
- Rearranging the equation to find LCM:
\[ \text{LCM}(kx, ky) = \frac{k^2xy}{z} \]
- Since \( z \) is the HCF, we can express LCM as:
\[ \text{LCM}(a, b) = \frac{(HCF \times x \times y)}{HCF} = \frac{z \times xy}{z} = xy \times z \]

6. **Final Result**:
- Thus, the LCM of the two numbers is:
\[ \text{LCM}(a, b) = xy \times z \]

### Conclusion:
The LCM of the two whole numbers given their ratio \( x : y \) and HCF \( z \) is:
\[ \text{LCM} = xy \times z \]