Least Common Multiple in JavaScript

"use strict";
// Least Common Multiple in JavaScript
//
// 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
// Node.js 18+: Int32Array inputs and workspaces provide compact integer storage. Automatic
// lengths and checked arithmetic reject values outside signed 32-bit. Invalid inputs or
// overflow throw RangeError.
//
// EXAMPLE
// Expected return: 36.
// Run: node example.js
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(valid) { if (!valid) throw new RangeError("invalid algorithm input"); }
function alg_checked(v) { if (!Number.isInteger(v) || v < -2147483648 || v > 2147483647) throw new RangeError("32-bit result overflow"); return v; }
function alg_add(a,b) { return alg_checked(a+b); }
function alg_sub(a,b) { return alg_checked(a-b); }
function alg_mul(a,b) { return alg_checked(a*b); }
function alg_size(n) { alg_require(Number.isInteger(n) && n>=0 && n<=4000000); return n; }

function lcm(a, b) {
    alg_require(Number.isInteger(a) && a >= -2147483648 && a <= 2147483647);
    alg_require(Number.isInteger(b) && b >= -2147483648 && b <= 2147483647);
    alg_require(((a >= 0) && (b >= 0)));
    if (((a == 0) || (b == 0))) {
        return 0;
    }
    let x = a;
    let y = b;
    let remainder = 0;
    while ((y != 0)) {
        remainder = (x % y);
        x = y;
        y = remainder;
    }
    return alg_mul(Math.floor(a / x), b);
}

let a = 12;
let b = 18;
let result = lcm(a, b);
console.log(result);