Why couldn't you do something like this? (There may be some subtle flaw I am missing, but it seems like it should work...)

use strict;
use warnings;
use Algorithm::Diff qw/LCS/;

my @s1 = split //, <DATA>;

while (<DATA>) {
    chomp;
    next unless length;
    my @s2 = split //, $_;
    @s1 = LCS( \@s1, \@s2 );
}

print @s1;

__DATA__
CPD6Z98SB2KQNWV0F7Y1IX4GLRA5MTOJHE3U
CXZOL6SUI2WTJ30HF519YPGBRNAK48MQVD7E
T8COSQU6I2FJN40DKL157WVGPYXARZ3MBHE9
KNCWVZDSR5420LP91FIQGB7Y3A6J8MOUXTEH
XF9C4PSDY62TWJ0QBN17IKG3OH8ALVRM5UEZ
D9QCHUSN7TW2YZL0O831FGXIR6JA4P5MVBKE
ZC7ISQUPK6N20OLV4T31G9FRXBAWM5YJHED8
Z3C7SJVODL25TRQ01HPWGNKXB4UA68YMI9EF
BC9OXDHS2FI5Z6U0TYL1VPGQK7ANR38MEWJ4
K4TCQBHS2ZV7FXU0P8R1YGDON3A6JILM9EW5
[download]