Assuming that you always want to split your net it /0, /8, /16, /24 blocks as your example suggests, the following code will work (not golfed, could certainly be made shorter; test ed a bit, but not all edge cases):

use strict;
use warnings;

my @ips = qw(1.2.3.4 1.2.3.5 1.2.3.7);

my $first = shift @ips;
my @identicals = split m/\./, $first;
for (@ips){
    my @b = split m/\./;
    for my $i (0 .. $#identicals){
        if ($b[$i] ne $identicals[$i]){
            splice @identicals, $i;
            last;
        }
    }
}

my @rest = (0) x (4 - @identicals);
my $net = join('.', @identicals, @rest) . '/' . (8 * @identicals);
print "$net\n";
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If you want it to work bit by bit instead, you have to map the IPs to binary representation first.

If somebody suggests a good module, you should use that instead.