What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

There are two ways to solve this. You can either brute force the numbers or find the LCM of the numbers 1 to 20. In this case, brute forcing would not be a smart method since the final answer is 232792560 and WILL take a long time in PHP.

**Brute Force PHP Script**

<?php $run = true; $count = 0; while($run) { $count++; $cur = 0; $i = 1; while($i < 21) { if($count % $i == 0) $cur++; else $i = 21; $i++; } if($cur == 20) { $run = false; } } echo $count; ?>

**Finding the LCM**

2 = 2 3 = 3 4 = 2 * 2 5 = 5 6 = 2 * 3 7 = 7 8 = 2 * 2 * 2 9 = 3 * 3 10 = 2 * 5 11 = 11 12 = 2 * 2 * 3 13 = 13 14 = 2 * 7 15 = 3 * 5 16 = 2 * 2 * 2 * 2 17 = 17 18 = 3 * 3 * 3 19 = 19 20 = 2 * 2 * 5 LCM = 2 * 2 * 2 * 2 * 3 * 3 * 5 * 7 * 11 * 13 * 17 * 19 = 232792560