Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2017, Director: Artur Travesa i Grau[en] The algorithm LLL is a strong tool for reducing lattice bases in polinomical time introduced by Arjen Lenstra, Hendrik Lenstra and László Lovász in 1982. We will study it’s implementation, as well as proof it’s polinomical time behaviour. Finally, we will show it’s use in factorizing factorizing polynomials with rational coefficients and some computational examples.