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: $\text{Option 1: 36}$