For the fun of it, I wanted to give the thing a closed, whole-integer form. The problem was, that a "close fitting" was wanted, and all I had was the following expression:

my $M;
my $n;
my $remaining = $n % $M;
my $next_multiple = $n + $M - $remaining;
[download]

This means, that my calculation always was one multiple too large whenever $remaining was zero. So I needed to fudge that a bit, by the idea that, if I made $n one smaller in one part, and added that one later on, I could maybe shift the error into the right direction:

for my $n (1..20) {
  print "$n:\t";
  for my $M (2..5) {
    my $remaining = ($n-1) % $M;  # subtract one from the remainder
    my $next_multiple = $n-1  + $M - $remaining;
    print "$next_multiple\t";
  };
  print "\n";
};
[download]

or, as my unreadable shell test expression:

perl -e "my $n=20; for(@ARGV){$x=$n-1+($_-($n-1)%$_);print qq($n\[$_] 
+:$x\n)}" 2 3 4 5 6 7 8 9 10

# resp.

$x=$n-1+($M-($n-1)%$M)
[download]

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