20. In the performance of a group gymnastics, it is required that when the formation changes to 10 rows, 15 rows, 18 rows, and 24 rows, the formation can always form a rectangle. How many people are needed at minimum for the group gymnastics performance?
20. Solution: Since the formation needs to be a rectangle, the number of people must be a multiple of the number of rows. Finding the minimum number of people is essentially finding the least common multiple (LCM) of the row numbers. Using the method of prime factorization, we get
$$\begin{array}{ll}
10=2 \times 5, & 15=3 \times 5 \\
18=2 \times 3^{2}, & 24=2^{3} \times 3
\end{array}$$

Therefore, $\{10,15,18,24\}=2^{3} \times 3^{2} \times 5=360$.
Answer: The minimum number of people required is 360.