Add solution 3 for project euler problem 5.

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() = }")