Problem 5 - Smallest Multiple

2520 is the smallest number that can be divided by each of the numbers from 1 to 10 without any remainder. What is the smallest positive number that is evenly divisible by all of the numbers from 1 to 20?

The Idea

This is equivalent to the problem of finding the least common multiple of numbers from 1 to 20. Stated differently, we are finding the least amount of times we need to include each prime in the prime factorization. For example,$2^4 = 16$ is the most number of times we have a factor of 2. While 3 has a max power of 2 under 20, and all primes greater than 3 have a maximum power of 1. Therefore, we multiply $2^4$ by $3^2$ and all of the other primes greater than 3 but less than 20 to find the final answer.