Python/project_euler/problem_005/sol2.py

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from maths.greatest_common_divisor import greatest_common_divisor
"""
Project Euler Problem 5: https://projecteuler.net/problem=5
Smallest multiple
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?
References:
- https://en.wiktionary.org/wiki/evenly_divisible
- https://en.wikipedia.org/wiki/Euclidean_algorithm
- https://en.wikipedia.org/wiki/Least_common_multiple
"""
def lcm(x: int, y: int) -> int:
"""
Least Common Multiple.
Using the property that lcm(a, b) * greatest_common_divisor(a, b) = a*b
>>> lcm(3, 15)
15
>>> lcm(1, 27)
27
>>> lcm(13, 27)
351
>>> lcm(64, 48)
192
"""
return (x * y) // greatest_common_divisor(x, y)
def solution(n: int = 20) -> int:
"""
Returns the smallest positive number that is evenly divisible (divisible
with no remainder) by all of the numbers from 1 to n.
>>> solution(10)
2520
>>> solution(15)
360360
>>> solution(22)
232792560
"""
g = 1
for i in range(1, n + 1):
g = lcm(g, i)
return g
if __name__ == "__main__":
print(f"{solution() = }")