RosettaCodeData/Task/Find-common-directory-path/Mathematica/find-common-directory-path....

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FindCommonDirectory[x_] := If[StringTake[#, -1] != "/", StringTake[#, Max[StringPosition[#, "/"]]], #] &
[Fold[LongestCommonSubsequence, First[x] , Rest[x]]]
FindCommonDirectory[{"/home/user1/tmp/coverage/test", "/home/user1/tmp/covert/operator", "/home/user1/tmp/coven/members"}]
->"/home/user1/tmp/"