Explanation:

- The numbers are in the ratio 1:2:3. Let's represent them as x, 2x, and 3x.

- According to the problem, their product is 1296:

$$ x \times 2x \times 3x = 1296 $$

$$ 6x^3 = 1296 $$

- Solve for \( x^3 \):

$$ x^3 = \frac{1296}{6} $$

$$ x^3 = 216 $$

- Calculate \( x \):

$$ x = \sqrt[3]{216} $$

$$ x = 6 $$

- Find the three numbers:

- First number: \( x = 6 \)

- Second number: \( 2x = 12 \)

- Third number: \( 3x = 18 \)

- Calculate their sum:

- \( 6 + 12 + 18 = 36 \)

- Correct Answer: \(\color{green}{\text{Option 1: 36}}\)