Refactor LCM: rename to Lcm, add docs, simplify

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

Author: williamfiset

README.md

@@ -250,7 +250,7 @@ $ java -cp classes com.williamfiset.algorithms.search.BinarySearch
 - [Fast Fourier transform (quick polynomial multiplication, complex numbers)](src/main/java/com/williamfiset/algorithms/math/FastFourierTransformComplexNumbers.java) **- O(nlog(n))**
 - [Primality check](src/main/java/com/williamfiset/algorithms/math/IsPrime.java) **- O(√n)**
 - [Primality check (Rabin-Miller)](src/main/java/com/williamfiset/algorithms/math/RabinMillerPrimalityTest.py) **- O(k)**
-- [Least Common Multiple (LCM)](src/main/java/com/williamfiset/algorithms/math/LCM.java) **- ~O(log(a + b))**
+- [Least Common Multiple (LCM)](src/main/java/com/williamfiset/algorithms/math/Lcm.java) **- ~O(log(a + b))**
 - [Modular inverse](src/main/java/com/williamfiset/algorithms/math/ModularInverse.java) **- ~O(log(a + b))**
 - [Prime factorization (pollard rho)](src/main/java/com/williamfiset/algorithms/math/PrimeFactorization.java) **- O(n<sup>1/4</sup>)**
 - [Relatively prime check (coprimality check)](src/main/java/com/williamfiset/algorithms/math/RelativelyPrime.java) **- ~O(log(a + b))**

src/main/java/com/williamfiset/algorithms/math/BUILD

@@ -49,10 +49,10 @@ java_binary(
     runtime_deps = [":math"],
 )
 
-# bazel run //src/main/java/com/williamfiset/algorithms/math:LCM
+# bazel run //src/main/java/com/williamfiset/algorithms/math:Lcm
 java_binary(
-    name = "LCM",
-    main_class = "com.williamfiset.algorithms.math.LCM",
+    name = "Lcm",
+    main_class = "com.williamfiset.algorithms.math.Lcm",
     runtime_deps = [":math"],
 )
 

src/main/java/com/williamfiset/algorithms/math/LCM.java

@@ -0,0 +1,30 @@
+/**
+ * Computes the Least Common Multiple (LCM) of two numbers using the relation LCM(a, b) = |a /
+ * gcd(a, b) * b|.
+ *
+ * <p>Time: ~O(log(a + b))
+ *
+ * @author William Fiset, william.alexandre.fiset@gmail.com
+ */
+package com.williamfiset.algorithms.math;
+
+public class Lcm {
+
+  /** Returns the least common multiple of a and b. The result is always non-negative. */
+  public static long lcm(long a, long b) {
+    return Math.abs(a / gcd(a, b) * b);
+  }
+
+  private static long gcd(long a, long b) {
+    if (b == 0)
+      return Math.abs(a);
+    return gcd(b, a % b);
+  }
+
+  public static void main(String[] args) {
+    System.out.println(lcm(12, 18));   // 36
+    System.out.println(lcm(-12, 18));  // 36
+    System.out.println(lcm(12, -18));  // 36
+    System.out.println(lcm(-12, -18)); // 36
+  }
+}