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Found problems: 76

2016 May Olympiad, 1
Tags: perfect cube , number theory
Seven different positive integers are written on a sheet of paper. The result of the multiplication of the seven numbers is the cube of a whole number. If the largest of the numbers written on the sheet is $N$, determine the smallest possible value of $N$. Show an example for that value of $N$ and explain why $N$ cannot be smaller.