Caching plays a crucial role in networking systems to reduce the load on the network and is commonly employed by content delivery networks (CDNs) to improve performance. One of the commonly used mechanisms, Least Recently Used (LRU), works well for identical file sizes. However, for asymmetric file sizes, the performance deteriorates. This article proposes an adaptation to the LRU strategy, called gLRU, where the file is sub-divided into equal-sized chunks. In this strategy, a chunk of the newly requested file is added in the cache, and a chunk of the least-recently-used file is removed from the cache. Even though approximate analysis for the hit rate has been studied for LRU, the analysis does not extend to gLRU, since the metric of interest is no longer the hit rate as the cache has partial files. This article provides a novel approximation analysis for this policy where the cache may have partial file contents. The approximation approach is validated by simulations. Further, gLRU outperforms the LRU strategy for a Zipf file popularity distribution and censored Pareto file size distribution for the file download times. Video streaming applications can further use the partial cache contents to help the stall duration significantly, and the numerical results indicate significant improvements (32%) in stall duration using the gLRU strategy as compared to the LRU strategy. Furthermore, the gLRU replacement policy compares favorably to two other cache replacement policies when simulated on MSR Cambridge Traces obtained from the SNIA IOTTA repository.