We show that a constant factor approximation of the shortest and closest lattice vector problem in any l(p)-norm can be computed in time 2((0.802 + epsilon)n). This matches the currently fastest constant factor approximation algorithm for the shortest vector problem in the l(2) norm. To obtain our result, we combine the latter algorithm for l(2) with geometric insights related to coverings. (C) 2021 Published by Elsevier Inc.