12. Find the unit digit of $17^{17} \times 19^{19} \times 23^{23}$.
12. Answer: 1
$$
\begin{array}{l}
17^{17}=7^{17}=7(\bmod 10) \\
19^{19} \equiv 9^{19} \equiv 9(\bmod 10) \\
23^{23} \equiv 3^{23} \equiv 7(\bmod 10)
\end{array}
$$

Since $7 \times 9 \times 7=441=1(\bmod 10)$, the unit digit is 1 .