Example 15 There are three workers transporting bricks from the brick pile to the scaffolding for wall construction. It takes Worker A 15.6 minutes, Worker B 16.8 minutes, and Worker C 18.2 minutes for a round trip. Now, all three start from the brick pile at the same time. What is the minimum number of minutes it will take for all three to return to the brick pile at the same time?
To find the minimum number of minutes required for the three people to return to the brick pile simultaneously, we need to find the least common multiple (LCM) of $15.6, 16.8$, and $18.2$. Since
$$\left.\begin{array}{c|c|c}
15.6 & 16.8 \\
15.6 & 15.6 \\
\hline 0 & 1.2
\end{array} \right\rvert\,$$

Thus, $(15.6, 16.8) = 1.2$. By Lemma 10, we have
$$\{15.6, 16.8\} = \frac{15.6 \times 16.8}{1.2} = 218.4$$

Since $\frac{218.4}{18.2} = 12$, it follows that $\{15.6, 16.8, 18.2\} = 218.4$.
Therefore, the minimum time required is 218.4 minutes, which is 3 hours and 38.4 minutes for the three people to return to the brick pile simultaneously.