We propose K-Closest Points (KCP), an efficient and effective laser scan matching approach inspired by LOAM and TEASER++. The efficiency of KCP comes from a feature point extraction approach utilizing the multi-scale curvature and a heuristic matching method based on the $k$-closest points. The effectiveness of KCP comes from the integration of the feature point matching approach and the maximum clique pruning. We compare KCP against well-known scan matching approaches on synthetic and real-world LiDAR data (nuScenes dataset). In the synthetic data experiment, KCP-TEASER reaches a state-of-the-art root-mean-square transformation error $(0.006\,\mathrm{m}, 0.014^\circ)$ with average computational time $49\mathrm{ms}$. In the real-world data experiment, KCP-TEASER achieves an average error of $(0.018\,\mathrm{m}, 0.101^\circ)$ with average computational time $77\,\mathrm{ms}$. This shows its efficiency and effectiveness in real-world scenarios. Through theoretic derivation and empirical experiments, we also reveal the outlier correspondence penetration issue of the maximum clique pruning that it may still contain outlier correspondences.