Here is a bad solution just for variety.

my $sep = chr(033);
my $str = join $sep, @files;
if ($str =~ /^([^$sep]*)[^$sep]*($sep\1[^$sep]*)*\z/s) {
  print "Common substring: '$1'\n";
}
else {
  die "Pattern unexpectedly failed to match?";
}
[download]

Of course it assumes that chr(033) does not appear in the strings...