Explanation:

- The product of two numbers is equal to the product of their LCM (L) and HCF (H).

- Given the ratio L : H = 3 : 2, we can express L = 3k and H = 2k for some constant k.

- The product of the numbers is L × H = (3k) × (2k) = 6k^2.

- We also know from the problem statement that the sum of the numbers is 45.

- Without specific values for the individual numbers, we cannot directly find k from the sum.

- Option 1, 243: This would imply a specific k value, but not enough data to isolate k.

- Option 2, 486: This would imply k = 9, since 6k^2 = 486 results in k^2 = 81.

- Option 3, 504: This suggests a different k value.

- Option 4, "Cannot be determined": The reasoning can find a definite answer under the given conditions.

Therefore, the correct answer is option 2 - 486.