What is the smallest integer you would need to multiply to $${{\mathtt{2}}}^{{\mathtt{9}}}{\mathtt{\,\times\,}}{{\mathtt{3}}}^{{\mathtt{14}}}{\mathtt{\,\times\,}}{{\mathtt{5}}}^{{\mathtt{15}}}{\mathtt{\,\times\,}}{{\mathtt{6}}}^{{\mathtt{3}}}$$ for it to become a perfect square? Show how you determined the number needed.
