Explanation:

To determine the correct HCF of the two numbers, let's understand the relationship between LCM, HCF, and the product of two numbers:

- The formula linking these is:

$$

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

$$

- Given that:

$$

\text{LCM} = 450

$$

$$

\text{Product of the two numbers} = 20250

$$

- Plugging in these values into the formula gives:

$$

450 \times \text{HCF} = 20250

$$

- Solving for HCF:

$$

\text{HCF} = \frac{20250}{450} = 45

$$

- Therefore, option 4: 45 is the correct HCF.

Option breakdown:

- Option 1: 90 – Incorrect, HCF is lower.

- Option 2: 15 – Incorrect, HCF is higher.

- Option 3: 150 – Incorrect, too high.

- Option 4: 45 – Correct, matches calculation.