Adding best practices (Local filehandles, error checking), and efficiency to your code, and adding a zero value check as the OP requested:

#!/usr/bin/perl
use strict;
use warnings;

my $input = 'input.txt';
my $output = 'output.txt';
my $constant = 15; #number you are multiplying by
my $minimum  = 20; # Smallest number to multiply
my $zero_replace = 666; # Replacement for zero

open my $in, "<", $input or die "Could not open $input for reading:$!"
+;
open my $out, ">>", $output or die "Could not open $output for append:
+$!";
while (<$in>){
  chomp $_;
  $_ = $zero_replace if 0 == $_; # 
  next if $_ < $minimum;
  print $out ($_ * $constant),"\n";
}
close $in;
close $out;
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