Question

( Problema nr,1 ) Aflati perechile de numere naturale care satisfac simultan conditiile :
a) au suma 30 si c.m.m.m.d.c. 5 ;
b) au suma 75 si c.m.m.d.c. 15 ;
c) au suma 120 si c.m.m.d.c. 12 ;
d) au produsul 250 si c.m.m.d.c. 5 ;
e) au produsul 600 si c.m.m.d.c. 10 ;

Answer 1

a)ca sa aiba c.m.m.d.c 5 sunt nr:5,10,15,20,...
5+10+15=30
20+10=30
b)ca sa ai ba c.m.m.d.c 15  sunt nr:15,30,45,60,...
30+45=75
60+15=75
c)ca sa aiba c.m.m.d.c 12 sunt nr:12,24,36,48,60,72,84,96,...
72+48=120
36+84=120
d)ca sa aiba c.m.m.d.c 5 sunt nr:5,10,15,20,

Answer 2

a) 5+25=30  cmmdc  5=5
                                 25=5²
                                 cmmdc -5
ce inseana cmmdc ?nr.se descompun in factori iar dupa descompunere se ia nr.comun la puterea cea mai mica
b) 15+60 =75  15 =3*5
                        60=2²*3*5
                        cmmdc=3*5=15
c)108+12=120   108=2²*3³
                           12=2²*3
                           cmmdc=2²*3=12
d)25*10=250    25=5²
                        10=2*5
                           cmmdc=5
e)60*10=600    60=2²*3*5
                         10=2*5
                        cmmdc=2*5=10