Important scientific number

Pin was assembling his new, highly important invention. However, at some point, he noticed an error in one of the formulas, which might have caused him to assemble one of the components incorrectly.

After carefully examining the component and correcting the formula, Pin discovered that it contained two gears with $a$ and $b$ teeth, respectively. For the component to function correctly, the gears should have sizes a + x and b + x, where $x$ is a non-negative integer that satisfies the following conditions:

• a + x is divisible by $b$;

• b + x is divisible by $a$.

Pin is very tired and asks for help in finding the smallest suitable value of $x$. Since he does not like overly large gears, the smallest possible $x$ should be chosen among all valid options.