Question

Determinati numerele naturale a si b nenule stiind ca : b) (a,b)=15 [a,b]=90; (a,b)=15; a+b=105

Answer 1

(a, b) =15 -› a = 15k
b = 15x

a•b = (a,b) • [a,b]
-› 15k• 15x = 15• 90
-› 225• k• x = 1350
-› k• x = 1350 : 225
-›k• x = 6

primul caz :
k = 1 -› a = 15 si
x = 6 -› b = 90 invers

al 2 lea caz :
k = 2 -› a = 30 si
x = 3 -› b = 45 invers