Question

Aflati nr a si b stiind ca [a,b]=72 si a*b=864

Answer 1

an=72
bm=72
ab=72^2/mn
864=72^2/mn
mn=6
m=1, n=6, a=12, b=72
m=2, n=3, a=36, b=24
m=3, n=2, a=24, b=36
m=6, n=1, a=72, b=12

Answer 2

 (a,b)=864:72=12;
a=12x; b=12y; (x,y)=1.
 a·b = 12x·12y=864
x·y=864:144=6
Posibilitati:
a) y=1⇒x=6;  a=12·6=72; b=12·1=12;   (72,12)
b) y=2⇒x=3;  a=12·3=36; b=12·2=24;  (36,24)
c) y=3⇒x=2;  a=12·2=24; b=12·3=36;  (24,36)
d) y=6⇒x=1;  a=12·1=12; b=12·6=72;  (12,72)