def sum_of_multiples(maximum, divisor_one, divisor_two):
"""
Function returns sum of all multiples of divisor_one and divisor_two less
than or equal to the maximum.
Uses the principle of summation from 1 to n ( n(n+1)/2 ), therefore the sum of all multiples
of k to m is ( km(m+1)/2 ), where m is the number of times k goes into the max (n).
REQ: max, divisor_one, divisor_two >= 1
REQ: type(max, divisor_one, divisor_two) == int
:param maximum: {int} is maximum int to sum to
:param divisor_one: {int} is first multiple to sum
:param divisor_two: {int} is second multiple to sun
:return: {int} sum of all multiples of divisor_one and divisor_two to maximum
"""
# check input, raise relevant errors
if type(maximum) != int or type(divisor_one) != int or type(
divisor_two) != int:
raise TypeError("One of input params was not type of int")
if maximum <= 0 or divisor_one <= 0 or divisor_two <= 0:
raise ValueError("One of input params was a negative/zero value")
# get whole number of times each divisor goes into max
quotient_one = maximum // divisor_one
quotient_two = maximum // divisor_two
# get lcm of divisor_one & divisor_two, as this will be double counted
lcm = least_common_multiple(divisor_one, divisor_two)
lcm_quotient = maximum // lcm
# get divisor and lcm sums
divisor_one_sum = divisor_one * summation(quotient_one)
divisor_two_sum = divisor_two * summation(quotient_two)
lcm_sum = lcm * summation(lcm_quotient)
# add quotient sums and subtract lcm sum
return divisor_one_sum + divisor_two_sum - lcm_sum
def test_input_one(self):
self.assertEqual(least_common_multiple(11, 1), 11)
def test_input_zero(self):
self.assertEqual(least_common_multiple(11, 0), 0)
def test_two_primes(self):
self.assertEqual(least_common_multiple(11, 7), 77)
def test_one_prime(self):
self.assertEqual(least_common_multiple(11, 4), 44)
def test_same_input(self):
self.assertEqual(least_common_multiple(15, 15), 15)
def test_input_is_return(self):
self.assertEqual(least_common_multiple(15, 3), 15)
def test_regular(self):
self.assertEqual(least_common_multiple(4, 3), 12)