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Practitioners lined up in rectangle with row with four, five or six exercisers, one always missing to full rectangle. How many exercisers were on the field, if they have estimated not been more than 100?

Correct result:

n =  59

Solution:

$$\begin{gathered} 4=2^2 \\ 5\mathrm{.}\mathrm{.}\mathrm{.}\text{ prime number } \\ 6=2\cdot 3 \\ LCM(4,5,6)=2^2\cdot 3\cdot 5=60 \\ n=LCM(4,5,6)-1=59 \end{gathered}$$

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