Question

determinati numerele naturale a si b , nenule , stiind ca :
(a,b)= 12 :[a,b]= 72

Answer 1

a=12y;⇒b=12z;
a=72/m⇒b=72/n;
⇒12y=72/m⇒72=12y·m⇒y·m=6;
⇒12z=72/n⇒72=12z·n⇒z·n=6;
⇒y·m=6⇒y,m∈[[1,6],[2,3],[3,2],[6,1]];
⇒z·n=6⇒z,n∈[[1,6],[2,3],[3,2],[6,1]];
⇒a∈[12,24,36,72];
⇒b∈[12,24,36,72];