Array of arrays is probably the best data structure. The trick in using it is to pull elements off the front of each nested array to get the output data as you need it:

#use strict;
use warnings;

my $File1 = <<FILE;
13
34
32
20
43
FILE

my $File2 = <<FILE;
22
15
27
33
48
65
34
FILE

my $File3 = <<FILE;
18
20
22
45
44
32
12
26
FILE

my @data;

for my $file (\$File1, \$File2, \$File3) {
    open my $fIn, '<', $file or die "Can't open $file: $!\n";
    
    push @data, [];
    
    while (<$fIn>) {
        chomp;
        push @{$data[-1]}, $_;
    }
}

while (grep {@$_} @data) {
    printf "%s\n", join "\t", map {$_ // ''} map {shift @$_} @data;
}
[download]

Prints:

13    22    18
34    15    20
32    27    22
20    33    45
43    48    44
    65    32
    34    12
        26
[download]