#!/usr/bin/env python
"""
Created on 23 Apr 2017

@author: David Doblas Jiménez
@email: daviddoji@pm.me

Solution for problem 5 of Project Euler
https://projecteuler.net/problem=5
"""

from math import gcd

from utils import timeit

# The LCM of two natural numbers x and y is given by:
# def lcm(x, y):
#    return x * y // math.gcd(x, y)

# It is possible to compute the LCM of more than two numbers by iteratively
# computing the LCM of two numbers, i.e. LCM(a, b, c) = LCM(a, LCM(b, c))


@timeit("Problem 5")
def compute():
    """
    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?
    """

    ans = 1
    for i in range(1, 21):
        ans *= i // gcd(i, ans)

    return ans


if __name__ == "__main__":
    print(f"Result for problem 5 is {compute()}")