Let $x=0.\overline{12}$.
Then $100x=12.\overline{12}$.
Subtracting $x$ from $100x$, we get $99x=12$, so $x=\frac{12}{99}=\frac{4}{33}$.
The sum of the numerator and denominator is $4+33=\boxed{37}$.
The answer is: 37
Below is a math problem. Provide a detailed, step-by-step solution.

### Problem:
When the repeating decimal $0.\overline{12}$ is expressed as a common fraction in lowest terms, what is the sum of its numerator and denominator?

### Answer:
