Do day 8 and add gcm and prime factors to lib.

lib.py

@@ -1,5 +1,37 @@
 import re
 
+def prime_factors(n):
+    """
+    Returns a list of prime factors for n.
+
+    :param n: number for which prime factors should be returned
+    """
+    factors = []
+    rest = n
+    divisor = 2
+    while rest % divisor == 0:
+        factors.append(divisor)
+        rest //= divisor
+    divisor = 3
+    while divisor * divisor <= rest:
+        while rest % divisor == 0:
+            factors.append(divisor)
+            rest //= divisor
+        divisor += 2
+    if rest != 1:
+        factors.append(rest)
+    return factors
+
+def lcm(numbers: list[int]) -> int:
+    fs = []
+    for n in numbers:
+        fs += prime_factors(n)
+    s = 1
+    fs = list(set(fs))
+    for f in fs:
+        s *= f
+    return s
+
 def str_to_single_int(line: str) -> int:
     line = line.replace(" ", "")
     r = re.compile(r"\d+")