I followed Limbic~Region's advice and used String::LCSS_XS.

#!/usr/bin/perl

use strict;
use warnings;
use String::LCSS_XS qw(lcss lcss_all);

my @result = lcss (
    '1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 2 18 19 20 21 22 23 7 2
+4',
    '1 2 3 4 5 6 7 8 9 11 12 13 10 14 15 16 17 2 18 19 20 21 22 23 7 2
+4');

print "$result[0]\n";
[download]