Question

Verifică egalitatea (a;b)*[a;b]=a*b pentru fiecare pereche de numere indicată:
a) a=12;b=20
b) a=27;b=36
c) a=18;b=36
d) a=45;b=72

Answer 1

a) a=12;b=20
12=2²×3
20=2²×5
(12,20)=2²=4
[12,20]=2²×3×5=60
(12,20)×[12,20]=12×20
4×60=240
240=240

b)27=3³
36=2²×3²
(27,36)=3²=9
[27,36]=2²×3³=108
(27,36)×[27,36]=27×36
9×108=27×36
972=972

c)a=18, b=36
18=2×3²
36=2²×3²
(18,36)=2×3²=18
[18,36]=2²×3²=36
(18,36)×[18,36]=18×36
18×36=18×36
648=648

d)a=45, b=72
45=3²×5
72=2³×3²
(45,72)=3²=9
[45,72]=5×2³×3²=360
(45,72)×[45,72]=45×72
9×360=45×72
3240=3240