The lattice reduction method proposed by Lenstra, Lenstra and Lovasz (LLL algorithm) is employed to perform signal precoding in multiuser downlink communications. Efficient implementations of this method have been well investigated, which, as the original algorithm, provide a matrix that contains the transformations to be done over the initial channel matrix in order to get a transformed matrix with less correlated columns. Since there are several precoding algorithms that also make use of the inverse of the channel transformation matrix, in this work we use an efficient way to calculate the inverse of the transformation matrix inside the LLL algorithm. The impact of the preprocessing computational cost reduction in the overall cost of some well-known precoding algorithms is also discussed. In addition, both a computational cost and a performance comparison among the algorithms is included.