Ian Dorian Macleod
Problem 5
Problem Statement

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?

url: https://projecteuler.net/problem=5
Python implementation

import math

res = 0

def divisors(x):
    for i in range(1,21):
        if x % i != 0:
            return False
    return True

def find_min(maxint):
    res = 2
    for i in range(3,maxint+1):
        prime = True
        for j in range(2, i):
            if i % j == 0:
                prime = False
        if prime == True:
            res = res * i

    # check if current min satisfies divisibility for all ints
    for k in range(1, maxint+1):
        if res % k != 0: 
            # now find smallest prime factor in i and multiply
            # total value by that
            for g in range(2, k):
                if k % g == 0:
                    res = res * g
    return res
res = find_min(20)
print("Answer is " + str(res))
You can also download the source code for this problem here and compile it on your local machine.
Further Analysis