For a set of mulitple sequences, their patterns,Longest Common Subsequences (LCS) and Shortest Common Supersequences (SCS) represent different aspects of these sequences profile, and they can all be used for biological sequence comparisons and analysis. Revealing the relationship between the patterns and LCS,SCS might provide us with a deeper view of the patterns of biological sequences, in turn leading to better understanding of them. However, There is no careful examinaton about the relationship between patterns, LCS and SCS. In this paper, we have analyzed their relation, and given some lemmas. Based on their relations, a set of algorithms called the PALS (PAtterns by Lcs and Scs) algorithms are propsoed to discover patterns in a set of biological sequences. These algorithms first generate the results for LCS and SCS of sequences by heuristic, and consequently derive patterns from these results. Experiments show that the PALS algorithms perform well (both in efficiency and in accuracy) on a variety of sequences. The PALS approach also provides us with a solution for transforming between the heuristic results of SCS and LCS.