Multi-view clustering (MVC) optimally integrates complementary information from different views to improve clustering performance. Although demonstrating promising performance in many applications, we observe that most of existing methods directly combine multiple views to learn an optimal similarity for clustering. These methods would cause intensive computational complexity and over-complicated optimization. In this paper, we theoretically uncover the connection between existing k-means clustering and the alignment between base partitions and consensus partition. Based on this observation, we propose a simple but effective multi-view algorithm termed {Multi-view Clustering via Late Fusion Alignment Maximization (MVC-LFA)}. In specific, MVC-LFA proposes to maximally align the consensus partition with the weighted base partitions. Such a criterion is beneficial to significantly reduce the computational complexity and simplify the optimization procedure. Furthermore, we design a three-step iterative algorithm to solve the new resultant optimization problem with theoretically guaranteed convergence. Extensive experiments on five multi-view benchmark datasets demonstrate the effectiveness and efficiency of the proposed MVC-LFA.