from lib_prime import prime_factors_count
from lib_misc import product


def get_number_divisible(n):
    """ Returns the lowest number that is divisible
    by all numbers from 1 to n.  We calculate the factors
    for all numbers and make sure that the minimum number
    for each factor is included in the solution. """
    f = {}
    for i in range(2, n + 1):
        for prime, count in prime_factors_count(i).items():
            try:
                f[prime] = max(f[prime], count)
            except KeyError:
                f[prime] = count
    n = product([prime**count for prime, count in f.items()])
    return n


assert(get_number_divisible(10) == 2520)


def euler_005():
    return get_number_divisible(20)


assert(euler_005() == 232792560)
print("e005.py: {}".format(euler_005()))