I\'m familiar with LCS algorithms for 2 strings. Looking for suggestions for finding common substrings in 2..N strings. There may be multiple common substrings in each pair.
SUffix trees are the answer unless you have really large strings where memory becomes a problem. Expect 10~30 bytes of memory usage per character in the string for a good implementation. There are a couple of open-source implementations too, which make your job easier.
There are other, more succint algorithms too, but they are harder to implement (look for "compressed suffix trees").