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# help pls

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$$What is the smallest positive integer n such that 3n is a perfect square and 2n is a perfect cube?$$

Aug 4, 2021

#1
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What is the smallest positive integer $$n$$ such that
$$3n$$ is a perfect square and
$$2n$$ is a perfect cube?

My attempt:

$$\begin{array}{|rcll|} \hline 3n &=& 3*&3*2*3*2*3 =2^2(3^2)^2=324=18^2 \\ 2n &=& 2*&3*2*3*2*3 =2^33^3=216=6^3 \\ \hline n &=& & 3*2*3*2*3 = 108 \\ \hline \end{array}$$

Aug 5, 2021