# Matches

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

Result

n =  24

#### Solution:

$3 \ ... \ prime number \ \\ 4=2^2 \ \\ 6=2 \cdot 3 \ \\ 8=2^3 \ \\ LCM(3, 4, 6, 8)=2^3 \cdot 3=24 \ \\ \ \\ n=LCM(3,4,6,8)=24$

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