Question

1. Aflati c.m.m.d.c si c.m.m.m.c. pentru: a) 48,72,120; b) 507,910, 312; c) 54, 21, 140;


2. Sa se afle cel mai mic numar care prin impartirea pe rand la 9,12, si 15 sa dea de fiecare data
11
a) restul 7, catul diferit de zero.

Answer 1

Rezolvarea completa in atasament

Answer 2

12y=D48=1,2,3,4,6,8,12,16,24,48.
D72=1,2,3,4,6,8,9,12,18,24,36,72.
D120=1,2,3,4,5,6,8,10,12,15,20,24,30,40,60,120.
D48 ∩ D72 ∩ D120=1,2,3,4,6,8,12,24.
c.m.m.d.c.=24.
48=2^4×3
72=2^3×3^2
120=2^3×5×3
c.m.m.m.c.=2^4×3^2×5=16×9×5=720

N=9x+7=12y+7=15z+7
9x=12y=15z
9=3^2
12=3×2^2
15=3×5
c.m.m.m.c.=3^2×2^2×5=9×4×5=180
180=9x
x=20
12y=180
y=15
15z=180
z=12
N=9×20+7=180+7=187