Gcd and LCM/ Nth root in Python

algebra/gcd/python/gcd.py

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+"""
+    euclid_gcd(0 is used to find the gcd of two numbers using euclidean algorithm
+    @input: a, b numbers
+    @output gcd(a,b)
+"""
+
+def euclid_gcd(a, b):
+    if a < b:
+        return euclid_gcd(b, a)
+
+    while b != 0:
+        (a, b) = (b, a%b)
+
+    return a

algebra/lcm/python/lcm.py

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+"""
+    euclid_gcd() is used to find the gcd of two numbers using euclidean algorithm
+    @input: a, b numbers
+    @output gcd(a,b)
+"""
+
+def euclid_gcd(a, b):
+    if a < b:
+        return euclid_gcd(b, a)
+
+    while b != 0:
+        (a, b) = (b, a%b)
+
+    return a
+"""
+    lcm() is used to return the least common multiple between two numbers
+    @input: a, b numbers
+    @output: lcm(a, b)
+"""
+
+def lcm(a, b):
+    gcd = euclid_gcd(a, b)
+    return (a*b)/gcd

algebra/nth_root/python/nth_root.py

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+"""
+   Find the nth root of a and return the integer component only
+   @input: number, root
+   @output: nth root of number
+"""
+def nth_root(a,n):
+    high = 1
+    while high ** n <= a:
+        high *= 2
+    low = high/2
+    while low < high:
+        mid = (low + high) // 2
+        if low < mid and mid**n < a:
+            low = mid
+        elif high > mid and mid**n > a:
+            high = mid
+        else:
+            return mid
+    return mid + 1