Question

cmmdc = 3×5
cmmmc = 3×5²
Sa se afle numerele.
Vreau rezolvarea nu doar raspunsul va rog

Answer 1

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)}