PHP - Euler #5 Problems :(

[Moonbat]

First off, here's the problem: "What is the smallest number divisible by each of the numbers 1 to 20?"

I went with the good ol' brute-force method. But after trying every combination of loops, if statements, etc. I can't get a working solution. Here's what I'm using so far.

<?php

set_time_limit(0);
for ($i=0; $i<=1000000; $i++) {
if (($i &#37; 2) == 0 && ($i % 3) == 0 && ($i % 4) == 0 && ($i % 5) == 0 && ($i % 6) == 0 && ($i % 7) == 0 && ($i % 8) == 0 && ($i % 9) == 0 && ($i % 10) == 0 && ($i % 11) == 0 && ($i % 12) == 0 && ($i % 13) == 0 && ($i % 14) == 0 && ($i % 15) == 0 && ($i % 16) == 0 && ($i % 17) == 0 && ($i % 18) == 0 && ($i % 19) == 0 && ($i % 20) == 0) {
echo "<h2>" . $i . "</h2>";
echo "<br>";
} else {
echo "";
}
}

?>
Even though my for loop goes up to 1,000,000, be assured I've tried up to 5,000,000. I doubt the smallest number that can be divided evenly by 1-20 is any bigger than 1,000,000. What is wrong with my script?

[~~smart~fool~~]

Sorry to hax you but

Rather than doing 11.6M iterations why not:

- find prime factors of each number - you nearly did this

- take the smallest necessary collection of those prime numbers (the highest power of each prime)

- multiply them up

And bingo: you have:

2*2*2*2 * 3*3 * 5 * 7 * 11 * 13 * 17 * 19 = 232,792,560

Finding prime factors is easy, and I think this would be more scalable

[Moonbat]

Thanks for the idea. I'll try to get it working :D

[~~smart~fool~~]

The Principle of Parsimony - It is pointless to do with more what is done with less