The longest common subsequence (LCS) is a practical metric for assessing code similarity. However, traditional LCS-based methods face challenges in scalability and in effectively capturing critical semantics for identifying code fragments that are textually different but semantically similar, due to their reliance on discrete representation-based token encoding. To address these limitations, this study proposes an LCS-oriented embedding method that encodes code into low-dimensional dense vectors, effectively capturing semantic information. This transformation enables the computationally expensive LCS calculation to be replaced with efficient vector arithmetic, further accelerated using an approximate nearest neighbor algorithm. To support this approach, an embeddable LCS-based distance metric is developed, as the original LCS metric is non-embeddable. Experimental results demonstrate that the proposed metric outperforms tree-based and literal similarity metrics in detecting complex code clones. In addition, two targeted loss functions and corresponding training datasets are designed to prioritize retaining critical semantics in the embedding process, allowing the model to identify textually different but semantically similar code elements. This improves performance in detecting complex code similarities. The proposed method demonstrates strong scalability and high accuracy in detecting complex clones. When applied to similar bug identification, it has reported 23 previously unknown bugs, all of which are confirmed by developers in real-world projects. Notably, several of these bugs are complex and challenging to detect using traditional LCS-based techniques.