List::Compare can be helpful here. Just send the references to those three hashes to List::Compare's get_intersection method and it'll return the keys that those hashes have in common:

use strict;
use warnings;
use List::Compare;

my %hash1 = ( A => 1,   B => 2,   C => 3,   D => 4 );
my %hash2 = ( C => 30,  D => 40,  A => 10,  B => 20 );
my %hash3 = ( F => 600, B => 200, A => 100, E => 500 );

my $lc = List::Compare->new( \%hash1, \%hash2, \%hash3 );
my @intersection = $lc->get_intersection;

if (@intersection) {
    for my $key (@intersection) {
        print "\%hash1: $key => $hash1{$key}\n";
        print "\%hash2: $key => $hash2{$key}\n";
        print "\%hash3: $key => $hash3{$key}\n";
        print "\n";
    }
}
else {
    print "The three hashes don't share any common keys.\n";
}
[download]

Output:

%hash1: A => 1
%hash2: A => 10
%hash3: A => 100

%hash1: B => 2
%hash2: B => 20
%hash3: B => 200
[download]