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In pervasive computing environments, Location-Based Services (LBSs) are becoming increasingly important due to continuous advances in mobile networks and positioning technologies. Nevertheless, the wide deployment of LBSs can jeopardize the location privacy of mobile users. Consequently, providing safeguards for location privacy of mobile users against being attacked is an important research issue. In this paper a new scheme for safeguarding location privacy is proposed. Our approach supports location K-anonymity for a wide range of mobile users with their own desired anonymity levels by clustering. The whole area of all users is divided into clusters recursively in order to get the Minimum Bounding Rectangle (MBR). The exact location information of a user is replaced by his MBR. Privacy analysis shows that our approach can achieve high resilience to location privacy threats and provide more privacy than users expect. Complexity analysis shows clusters can be adjusted in real time as mobile users join or leave. Moreover, the clustering algorithms possess strong robustness.