12. (8 points) A natural number when divided by 19 leaves a remainder of 9, and when divided by 23 leaves a remainder of 7. What is the smallest such natural number?
【Solution】Solution: Let this natural number be $x$
$$
x=19 m+9=23 n+7,
$$

Rearranging gives: $x-7=19 m+2=23 n$,
Since the two divisors differ by $23-19=4$, we find the minimum value,
$$
\begin{array}{l}
23 \times 10=19 \times 12+2, \\
x-7=230, \\
x=237,
\end{array}
$$

Answer: The smallest natural number is 237.
Therefore, the answer is: 237.