Question

Aflati numerele naturale a si b stiind ca (a,b) =12 si [a,b]=72

Answer 1

$Deci,~(a;b)=12 \Rightarrow \\ a=12x \\ b=12y,~ unde ~ (x;y)=1.$
$Stim~ca~[a;b]=12*x*y~\Rightarrow~12*x*y=72\Rightarrow~x*y=6.$
$Avem~cazurile: \\ x=1, ~ y=6 \Rightarrow \boxed{a=12;~b=72}(si~invers)\\ x=2,~y=3\Rightarrow \boxed{a=24;~b=48}(si~invers).$