For a number to be a multiple of 3, the sum of its digits must be a multiple of 3.
The sum of the digits of 412 is 4+1+2=7.
To make the sum a multiple of 3, we need to add a number that is congruent to 2 modulo 3.
The smallest positive integer that satisfies this condition is $\boxed{2}$.
The answer is: 2
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
Determine the smallest positive integer that, when added to 412, results in a multiple of 3.

### Answer:
