From 83ad045bda32554f5f7eebcabb654dfd142240cd Mon Sep 17 00:00:00 2001
From: mindaugl <mindelek@gmail.com>
Date: Wed, 21 May 2025 18:48:35 +0300
Subject: [PATCH] Add solution 3 for project euler problem 5.
---
project_euler/problem_005/sol3.py | 51 +++++++++++++++++++++++++++++++
1 file changed, 51 insertions(+)
create mode 100644 project_euler/problem_005/sol3.py
diff --git a/project_euler/problem_005/sol3.py b/project_euler/problem_005/sol3.py
new file mode 100644
index 000000000000..0ca9dd24f2ff
--- /dev/null
+++ b/project_euler/problem_005/sol3.py
@@ -0,0 +1,51 @@
+"""
+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?
+"""
+
+
+def solution(n: int = 20) -> int:
+ """
+ Find the smallest number for 'n'.
+ Iterate over each number up to n and add new factors
+ that is not included in previous numbers.
+
+ # >>> solution(10)
+ # 2520
+ # >>> solution(15)
+ # 360360
+ # >>> solution(22)
+ # 232792560
+ """
+
+ # factors = {}
+ factors = [0] * (n + 1)
+ ans = 1
+ for i in range(2, n + 1):
+ if factors[i] == 0:
+ f = i
+ for j in range(2, i):
+ if f == 1:
+ break
+ power = factors[j]
+ while power > 0:
+ if f % j == 0:
+ f //= j
+ power -= 1
+ else:
+ break
+ if f != 1:
+ factors[f] += 1
+ ans *= f
+ return ans
+
+
+if __name__ == "__main__":
+ print(f"{solution() = }")