Answer
The largest number of people that can be placed on each team is \[12\].
Work Step by Step
As the teams are divided into all-men and all-women teams so the total number of people must be a factor of both \[24\]and \[60\].
So, in order to find the largest possible size of the team, find Highest Common Factor (HCF) of \[24\]and\[60\].
Prime factorization of \[24\]and \[60\]:
\[\begin{align}
& 24={{2}^{3}}\times {{3}^{1}} \\
& 60={{2}^{2}}\times {{3}^{1}}\times {{5}^{1}} \\
\end{align}\]
Calculate Highest Common Factor(HCF) of \[24\] and \[60\]:
\[\begin{align}
& \text{HCF}\left( 24,60 \right)={{2}^{2}}\times {{3}^{1}} \\
& =12
\end{align}\]
Hence, the largest number of people that can be placed on each team is \[12\].
