For any m strings of total length n, we propose an O(mn log n)-time, O(n)-space algorithm that finds a maximal common subsequence of all the strings, in the sense that inserting any character in it no longer yields a common subsequence of them. Such a common subsequence could be treated as indicating a nontrivial common structure we could find in the strings since it is NP-hard to find any longest common subsequence of the strings.