notam numerele a si b
(a;b)=3•5; [a;b]=3•5²
=> a•b=(a;b)•[a;b]=3²•5³
(a;b)=3•5=> a=3•5•m si b=3•5•n; m si n sunt prime intre ele; (m,n)=1
=> a•b=3•5•m •3•5•n=3²•5²•m•n
3²•5²•m•n=3²•5³
=> m•n=5
m=1 si n=5; m=5 si n=1
=> a=3•5•1=15 si b=3•5•5=75
a=3•5•5=75 si b=3•5•1=15
(a;b) ∈ {(15; 75); (75;15)}
