The cardinal of the finitely generated free (n + l)-valued Lukasiewicz BCK- algebras has been determined by different authors only for some values of n. In this article we find the formula that allows its calculus for every value of n. By the application of this formula for n = 1, n = 2, we corroborate the results obtained by L. Iturrioz and A. Monteiro (Rev. Un. Mat. Argentina, 22 (1966), 146) and L. Iturrioz and O.Rueda (Discrete Math., 18 (1977), 35-44). In addition we generalize the results found by A. V. Figallo (Rev. Un. Mat. Argentina, 41, 4 (2000), 33-43).