From 310efd163049daa820e8c0979dda879fc2c756cb Mon Sep 17 00:00:00 2001
From: Sai Sravya Thumati
 <64857617+Sai-Sravya-Thumati@users.noreply.github.com>
Date: Mon, 6 Oct 2025 11:37:47 +0530
Subject: [PATCH 1/3] Making it more readable by adding necessary details!

---
 maths/basic_maths.py | 6 ++++++
 1 file changed, 6 insertions(+)

diff --git a/maths/basic_maths.py b/maths/basic_maths.py
index 833f31c18b9e..3d6bb7962048 100644
--- a/maths/basic_maths.py
+++ b/maths/basic_maths.py
@@ -4,6 +4,11 @@
 
 
 def prime_factors(n: int) -> list:
+    """
+    Uses a standard method of dividing by 2, then odd divisors up to sqrt(n).
+    Time Complexity: O(sqrt(n))
+    Space Complexity: O(log n) on average
+    """
     """Find Prime Factors.
     >>> prime_factors(100)
     [2, 2, 5, 5]
@@ -120,3 +125,4 @@ def euler_phi(n: int) -> int:
     import doctest
 
     doctest.testmod()
+

From 2edc2c6ffd78e75228e1daf10c422b4963bdc03f Mon Sep 17 00:00:00 2001
From: Sai Sravya Thumati
 <64857617+Sai-Sravya-Thumati@users.noreply.github.com>
Date: Mon, 6 Oct 2025 11:41:02 +0530
Subject: [PATCH 2/3] Adding new algorithms in here which are very necessary to
 know!

---
 maths/basic_maths.py | 37 +++++++++++++++++++++++++++++++++++++
 1 file changed, 37 insertions(+)

diff --git a/maths/basic_maths.py b/maths/basic_maths.py
index 3d6bb7962048..83a826974321 100644
--- a/maths/basic_maths.py
+++ b/maths/basic_maths.py
@@ -2,6 +2,42 @@
 
 import math
 
+def gcd(a: int, b: int) -> int:
+    """Calculate the Greatest Common Divisor (GCD) using Euclid's Algorithm.
+    >>> gcd(54, 24)
+    6
+    >>> gcd(10, 0)
+    10
+    >>> gcd(0, 10)
+    10
+    >>> gcd(0, 0)
+    Traceback (most recent call last):
+        ...
+    ValueError: At least one number must be non-zero
+    >>> gcd(-54, 24)
+    6
+    """
+    if a == 0 and b == 0:
+        raise ValueError("At least one number must be non-zero")
+    a, b = abs(a), abs(b)
+    while b:
+        a, b = b, a % b
+    return a
+
+
+def lcm(a: int, b: int) -> int:
+    """Calculate the Least Common Multiple (LCM) using GCD.
+    >>> lcm(12, 15)
+    60
+    >>> lcm(0, 10)
+    0
+    >>> lcm(-12, 15)
+    60
+    """
+    if a == 0 or b == 0:
+        return 0
+    return abs(a * b) // gcd(a, b)
+
 
 def prime_factors(n: int) -> list:
     """
@@ -126,3 +162,4 @@ def euler_phi(n: int) -> int:
 
     doctest.testmod()
 
+

From 327f69648d499cdefe3914ffd6ba6cd25e60afa2 Mon Sep 17 00:00:00 2001
From: "pre-commit-ci[bot]"
 <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Date: Mon, 6 Oct 2025 06:12:11 +0000
Subject: [PATCH 3/3] [pre-commit.ci] auto fixes from pre-commit.com hooks

for more information, see https://pre-commit.ci
---
 maths/basic_maths.py | 3 +--
 1 file changed, 1 insertion(+), 2 deletions(-)

diff --git a/maths/basic_maths.py b/maths/basic_maths.py
index 83a826974321..e00efc734e91 100644
--- a/maths/basic_maths.py
+++ b/maths/basic_maths.py
@@ -2,6 +2,7 @@
 
 import math
 
+
 def gcd(a: int, b: int) -> int:
     """Calculate the Greatest Common Divisor (GCD) using Euclid's Algorithm.
     >>> gcd(54, 24)
@@ -161,5 +162,3 @@ def euler_phi(n: int) -> int:
     import doctest
 
     doctest.testmod()
-
-