require "./euler"

def integer_factorization_divisible_by_all_up_to(n)
  result = {} of Euler::NumType => Euler::NumType
  (2..n).map do |i|
    Euler.prime_factorization(i).each do |prime, exponent|
      if !result.has_key?(prime) || (exponent > result[prime])
        result[prime] = exponent
      end
    end
  end
  result
end

def factors_to_int(factorization : Hash(Euler::NumType, Euler::NumType))
  factorization.map { |prime, exponent| prime ** exponent }.product
end

puts factors_to_int(integer_factorization_divisible_by_all_up_to(20))