\(What is the smallest positive integer $n$ such that $3n$ is a perfect square and $2n$ is a perfect cube?\)
+26367 What is the smallest positive integer \(n\) such that
\(3n\) is a perfect square and
\(2n\) is a perfect cube?
My attempt:
\( \begin{array}{|rcll|} \hline 3n &=& 3*&3*2*3*2*3 =2^2(3^2)^2=324=18^2 \\ 2n &=& 2*&3*2*3*2*3 =2^33^3=216=6^3 \\ \hline n &=& & 3*2*3*2*3 = 108 \\ \hline \end{array}\)
