The $H.C.F.$ of two expressions $p$ and $q$ is $1$. Their $L.C.M.$ is

If $(x-4)$ is the $G.C.D.$ of $x^{2}-x-12$ and $x^{2}-mx-8$,find the value of $m$.

Find the $L.C.M.$ of the polynomials: $16-4x^{2}$ and $x^{2}+x-6$.

Find the $L.C.M.$ of the polynomials $2x^{2}-3x-2$ and $x^{3}-4x^{2}+4x$.

Find the $G.C.D.$ of $8(x^{4}-16)$ and $12(x^{3}-8)$.

The $L.C.M.$ and $H.C.F.$ of two polynomials $p(x)$ and $q(x)$ are $36 x^{3}(x+a)(x^{3}-a^{3})$ and $x^{2}(x-a)$ respectively. If $p(x)=4 x^{2}(x^{2}-a^{2})$,find $q(x)$.