from collections import Counter
from functools import reduce
import util

target = 232792560

def smallest_multiple(nbrs):
    factors = None

    # get the prime factors of all nbrs, and keep the highest occurence of each unique prime factor
    # in each number
    for num in nbrs:
        nums = util.find_prime_factors(num)

        count = Counter(nums)

        if (factors == None):
            factors = count
        else:
            for key, value in count.items():
                if (not factors[key] or value > factors[key]):
                    factors[key] = value
    result = 1

    for key, value in factors.items():
        result *= key ** value

    return result

result = smallest_multiple(range(1, 21))

print(result)
print(result == target)