2 - 49 Find the smallest natural number $n$ that satisfies the following properties:
(1) The unit digit of $n$ is 6;
(2) If the unit digit 6 of $n$ is moved to the front of the other digits, the resulting new number is 4 times $n$.
[Solution] Let the required natural number be
$$n=10 x+6,$$

where $x$ is a natural number.
Let the number of digits of $n$ be $m$. According to the problem, we have
$$6 \cdot 10^{m-1}+x=4(10 x+6)$$

which gives
$$\begin{array}{l}
13 x=2 \cdot 10^{m-1}-8 \\
2 \cdot 10^{m-1}=13 x+8
\end{array}$$

Thus, we can divide the number $200 \cdots 0$ by 13 until the first remainder is 8. This way, we get the smallest natural number
$$x=15384 \text {. }$$

Therefore, the smallest natural number sought is 153846.