2. Find the smallest positive integer $x$ that satisfies $\frac{x}{2}+\frac{x}{3}+\frac{x}{4}+\frac{x}{5}+\frac{x}{6}$ is an integer.
2. 20 .

Simplifying and finding a common denominator, we get
$$
\text { original expression }=\frac{87 x}{60}=\frac{29 x}{20} \text {. }
$$

From the problem, we know that $\frac{29 x}{20}$ is an integer, so the smallest positive integer