6. Vitya found the smallest possible natural number, which when multiplied by 2 gives a perfect square, and when multiplied by 3 gives a perfect cube. What number did Vitya find?
6. The desired number contains the factors $2^{3}=8$ and $3^{2}=9$. Thus, the smallest number is $8 \cdot 9=72$. Then $72 \cdot 2=144=12^{2}$ and $72 \cdot 3=216=6^{3}$. The desired number is 72.