12. If $x \in \mathbf{R}$, then the function
$$
f(x)=2 \sin \frac{x}{2}+3 \cos \frac{x}{3}
$$

has the smallest positive period of $\qquad$ .
12. $12 \pi$.

Since the period of $2 \sin \frac{x}{2}$ is $4 \pi$, and the period of $3 \cos \frac{x}{3}$ is $6 \pi$, the period of the function $f(x)$ is $12 \pi$.