From 9d7733f0e44d1aa84d8241e07a2fdfd8e17ca589 Mon Sep 17 00:00:00 2001
From: CharlesCNorton <135471798+CharlesCNorton@users.noreply.github.com>
Date: Mon, 22 Jun 2026 10:19:08 -0400
Subject: [PATCH 1/2] Fix ZeroDivisionError on zero operands in
 least_common_multiple

least_common_multiple_slow raised ZeroDivisionError for a zero operand (0 % n in the loop guard), e.g. least_common_multiple_slow(0, 5), and least_common_multiple_fast raised it for (0, 0) via floor-division by gcd(0, 0) == 0. The least common multiple is 0 whenever an operand is 0 (consistent with math.lcm), so both functions return 0 in that case. Adds doctests covering the zero inputs.
---
 maths/least_common_multiple.py | 16 ++++++++++++++++
 1 file changed, 16 insertions(+)

diff --git a/maths/least_common_multiple.py b/maths/least_common_multiple.py
index a5c4bf8e3625..5e4f03988333 100644
--- a/maths/least_common_multiple.py
+++ b/maths/least_common_multiple.py
@@ -14,7 +14,15 @@ def least_common_multiple_slow(first_num: int, second_num: int) -> int:
     10
     >>> least_common_multiple_slow(12, 76)
     228
+    >>> least_common_multiple_slow(0, 5)
+    0
+    >>> least_common_multiple_slow(5, 0)
+    0
+    >>> least_common_multiple_slow(0, 0)
+    0
     """
+    if first_num == 0 or second_num == 0:
+        return 0
     max_num = first_num if first_num >= second_num else second_num
     common_mult = max_num
     while (common_mult % first_num > 0) or (common_mult % second_num > 0):
@@ -30,7 +38,15 @@ def least_common_multiple_fast(first_num: int, second_num: int) -> int:
     10
     >>> least_common_multiple_fast(12,76)
     228
+    >>> least_common_multiple_fast(0, 5)
+    0
+    >>> least_common_multiple_fast(5, 0)
+    0
+    >>> least_common_multiple_fast(0, 0)
+    0
     """
+    if first_num == 0 or second_num == 0:
+        return 0
     return first_num // greatest_common_divisor(first_num, second_num) * second_num
 
 

From 3fd97356f6acb62347262d2eb95b047a659a9c2b Mon Sep 17 00:00:00 2001
From: CharlesCNorton <machineelv@gmail.com>
Date: Thu, 25 Jun 2026 07:09:57 -0400
Subject: [PATCH 2/2] Add zero-operand cases to least_common_multiple unit test

---
 maths/least_common_multiple.py | 5 ++++-
 1 file changed, 4 insertions(+), 1 deletion(-)

diff --git a/maths/least_common_multiple.py b/maths/least_common_multiple.py
index 5e4f03988333..425cbf528ec3 100644
--- a/maths/least_common_multiple.py
+++ b/maths/least_common_multiple.py
@@ -75,8 +75,11 @@ class TestLeastCommonMultiple(unittest.TestCase):
         (12, 25),
         (10, 25),
         (6, 9),
+        (0, 5),
+        (5, 0),
+        (0, 0),
     )
-    expected_results = (20, 195, 124, 210, 1462, 60, 300, 50, 18)
+    expected_results = (20, 195, 124, 210, 1462, 60, 300, 50, 18, 0, 0, 0)
 
     def test_lcm_function(self):
         for i, (first_num, second_num) in enumerate(self.test_inputs):