Longest Common Prefix Array
From http://en.wikipedia.org/wiki/Suffix_array, we have that "The fact that the minimum lcp value belonging to a consecutive set of sorted suffixes gives the longest common prefix among all of those suffixes can also be useful." So in your case, the LCP between MISSISSIPPI and ISSIPPI is min(4, 0) = 0.
You can find the minimum in a range in time O(1) via http://en.wikipedia.org/wiki/Range_Minimum_Query, and there is a lot of info on alternative approaches if you look at the TopCoder link there.