Hmmm...I tried your code and I am confused by at least the outputs for some inputs. Maybe you have an explanation for the following result? (I must confess, I really tried the code out since I have never used ^N before, so I apologize if I'm missing something here).

sub lcs{
    our %subs = ();
    my $n = @_;
    shift =~ m[^.*(.+)(?{ $subs{ $^N }++ })(?!)] while @_;
    my @subs = sort{ length $b <=> length $a } 
                 grep{ $subs{ $_ } == $n } keys %subs;

    return wantarray ? @subs : $subs[ 0 ];
}

$" = ", ";
my @inputs = (
  ["ABCDEF", "BCD", "QXDAF"], #okay result
  ["AAAA", "AA"] #spurious result(???)
);
for (@inputs) {
  @subs = lcs @$_;
  print "@$_=>@subs\n";
}
__END__

__OUTPUT___
ABCDEF, BCD, QXDAF=>D
AAAA, AA=>AAA
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,welchavw