Let $p$-some prime $p|xy$ Let $v_p(x)=a,v_p(y)=b$ then $v_p(xy)=a+b$ and $v_p(GCM(x^7,y^4)*GCM(x^8,y^5))=v_p(GCM(x^7,y^4))+v_p(GCM(x^8,y^5))= min (7a,4b)+min(8a,5b)$ $min (7a,4b)+min(8a,5b)=a+b$ has solutions $b=14a$ or $a=8b$ then $v_p(xy)=15a$ or $9b$