Matches

George poured out-of-the-box matches and composed their triangles, and no match was left. Then he tried squares, hexagons, and octagons, and no match was left. How many matches must be at least in the box?

Final Answer:

n =  24

Step-by-step explanation:

$$\begin{gathered} 3...\text{ prime number} \\ 4=2^2 \\ 6=2\cdot 3 \\ 8=2^3 \\ LCM(3,4,6,8)=2^3\cdot 3=24 \\ n=LCM(3,4,6,8)=24 \end{gathered}$$

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