Question

verificati relatia a ori b = (a,b) ori [a,b] pt urmatoarele perechi de nr naturale: a = 12 , b= 15 , a = 48 si b = 80 , a = 225 si b = 75 . repede va rog frumos

Answer 1

1)
a=12
b=15

12=2²•3
15=3•5
————
(12;15)=3
[12;15]=2²•3•5=4•3•5=3•20=60

(a;b)•[a;b]=a•b
3•60=12•15
180=180 (A)

2)
a=48
b=80

48=2⁴•3
80=2⁴•5
————–
(48;80)=2⁴=16
[48;80]=2⁴•3•5=240

(a; b)•[a;b]=a•b
16•240=48•80
3840=3840 (A)

3)
a=225
b=75

225=3²•5²
75=3•5²
—————
(225;75)=3•5²=75
[225;75]=3²•5²=225

(a;b)•[a;b]=a•b
75•225=75•225
16875=16875 (A)