Example 4 Find the unit digit of the natural number $2^{100}+3^{101}+4^{100}$.
Solution: Notice that
$$
\begin{array}{l}
2^{100} \equiv 2^{1 \times 25} \equiv\left(2^{4}\right)^{25} \equiv 16^{25} \\
\equiv 6^{25} \equiv 6(\bmod 10), \\
3^{101} \equiv 3^{4 \times 25+1} \equiv\left(3^{4}\right)^{25} \times 3^{1} \\
\equiv 1^{25} \times 3^{1} \equiv 3(\bmod 10), \\
4^{102} \equiv 4^{2 \times 51} \equiv\left(4^{2}\right)^{51} \equiv 16^{51} \equiv 6(\bmod 10) . \\
\text { Therefore, } 2^{100}+3^{101}+4^{102} \equiv 6+3+6 \equiv 5(\bmod 10),
\end{array}
$$

Thus, the unit digit of the natural number $2^{100}+3^{101}+4^{102}$ is 5.