The LCM of two natural numbers is 432. Which of the following can be their HCF?

Options

A. 12
B. 34
C. 26
D. 32

Answer

To determine which of the given options can be the HCF (Highest Common Factor) of two natural numbers whose LCM (Lowest Common Multiple) is 432, we can use the relationship between LCM and HCF. The relationship states that:

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

Given that the LCM is 432, we can express this relationship as:

\[ 432 \times \text{HCF} = a \times b \]

Where \( a \) and \( b \) are the two natural numbers.

To find possible values for the HCF, we need to check if the HCF divides the LCM (432) evenly.

### Step-by-Step Solution:

1. **Identify the LCM**: The LCM of the two numbers is given as 432.

2. **List the options for HCF**: We need to check which of the given options can be the HCF. Let's assume the options are 12, 34, 26, and 32 (as inferred from the transcript).

3. **Check divisibility**:
- **Option 1: HCF = 12**
- Check if \( 432 \div 12 = 36 \) (which is a whole number).
- Since 36 is a whole number, 12 can be an HCF.

- **Option 2: HCF = 34**
- Check if \( 432 \div 34 \approx 12.71 \) (which is not a whole number).
- Since this is not a whole number, 34 cannot be an HCF.

- **Option 3: HCF = 26**
- Check if \( 432 \div 26 \approx 16.615 \) (which is not a whole number).
- Since this is not a whole number, 26 cannot be an HCF.

- **Option 4: HCF = 32**
- Check if \( 432 \div 32 = 13.5 \) (which is not a whole number).
- Since this is not a whole number, 32 cannot be an HCF.

4. **Conclusion**: The only option that divides 432 evenly is 12. Therefore, the possible HCF of the two numbers is 12.

### Final Answer:
The possible HCF of the two natural numbers whose LCM is 432 is **12**.