Least Common Multiple in C#

using System;
// Least Common Multiple in C#
//
// PURPOSE
// The least common multiple is the smallest nonnegative common multiple. For positive inputs
// it equals a divided by gcd(a,b), multiplied by b.
//
// METHOD
// Handle zero first. Compute the gcd with Euclid, divide before multiplying to reduce
// intermediate overflow, and return the product.
//
// COMPLEXITY
// O(log(min(a,b))) arithmetic steps, O(1) auxiliary space.
//
// CONTRACT
// Inputs are nonnegative. Returns 0 if either input is zero. The final product must fit the
// integer range.
// Public APIs infer array lengths except in C, which accepts pointer/length pairs. Vertex
// counts and matrix dimensions remain explicit. Arrays must contain signed 32-bit integers.
// Sorted order, correct tree topology, and caller-owned data-structure invariants are
// preconditions; checking them on every query would change query complexity.
// Scalar and shape checks are included. Value-range checks are included where needed to
// prevent invalid indexing or nontermination. Allocation sizes are capped at 4,000,000
// workspace entries. Arithmetic outside Python raises an error on 32-bit overflow; Python
// uses arbitrary precision. Native allocation failures propagate. In-place outputs may be
// partly updated after arithmetic failure. These are single-threaded, in-memory
// implementations.
//
// LANGUAGE DETAILS
// C# / .NET 10: ReadOnlySpan<int> inputs, Span<int> outputs, primitive workspace arrays,
// Array.BinarySearch for LIS, and checked integer arithmetic. Invalid arguments and overflow
// throw exceptions.
//
// EXAMPLE
// Expected return: 36.
// Run: Use Program.cs in a net10.0 console project; dotnet run.
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

class Program {
    static void alg_require(bool valid) { if (!valid) throw new ArgumentException("invalid algorithm input"); }
    static int alg_size(int n) { alg_require(n>=0 && n<=4000000); return n; }

    static int lcm(int a, int b) {
        checked {
            alg_require(((a >= 0) && (b >= 0)));
            if (((a == 0) || (b == 0))) {
                return 0;
            }
            int x = a;
            int y = b;
            int remainder = 0;
            while ((y != 0)) {
                remainder = (x % y);
                x = y;
                y = remainder;
            }
            return ((a / x) * b);
        }
    }

    static void Main() {
        int a = 12;
        int b = 18;
        int result = lcm(a, b);
        Console.WriteLine(result);
    }
}