Question

Verificați egalitatea (a,b)•[a,b]=a•bpenrru perechile de numere a =120si b=130

Answer 1

Salut!

$\text{ (a, b) inseamna c.m.m.d.c., adica cel mai mare divizor comun.}\\\text{ [a, b] inseamna c.m.m.m.c., adica cel mai mic multiplu comun.}$

Pentru a efectua c.m.m.d.c. si c.m.m.m.c., trebuie sa descompunem termenii a si b in numere prime:

a = 120 = 2³ × 3 × 5

b = 130 = 2 × 5² × 3

$\Rightarrow(a,b)=(120,130)=2\cdot5=10\\\Rightarrow[a,b]=[120,130]=2^3\cdot3\cdot5\cdot13=1560\\\\\Rightarrow(a,b)[a,b]=10\cdot1560=15600\\\\a\cdot b=120\cdot 130 = 15600\\\\\Rightarrow 15600 = 15600 \Rightarrow (a,b)[a,b]=ab$

-Luke48