Least Common Multiple in PHP

<?php
declare(strict_types=1);
// Least Common Multiple in PHP
//
// 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
// PHP 8.1+ on a 64-bit runtime: packed arrays, strict scalar types, read-only inputs by
// value using copy-on-write, references only for outputs, and checked 32-bit arithmetic.
// Invalid input and overflow throw exceptions. PHP arrays have higher overhead than native
// packed buffers in C/Java.
//
// EXAMPLE
// Expected return: 36.
// Run: php example.php
// Tests for this exact source artifact run before publication. The accompanying source
// archive includes unit cases, runtime results, and source hashes.

function alg_require(bool $valid): void { if (!$valid) throw new InvalidArgumentException("invalid algorithm input"); }
function alg_checked(int|float $v): int { if ($v < -2147483648 || $v > 2147483647 || floor($v) != $v) throw new OverflowException("32-bit result overflow"); return (int)$v; }
function alg_add(int $a,int $b): int { return alg_checked($a+$b); }
function alg_sub(int $a,int $b): int { return alg_checked($a-$b); }
function alg_mul(int $a,int $b): int { return alg_checked($a*$b); }
function alg_size(int $n): int { alg_require($n>=0 && $n<=4000000); return $n; }

function lcm(int $a, int $b): int {
    alg_require((($a >= 0) && ($b >= 0)));
    if ((($a == 0) || ($b == 0))) {
        return 0;
    }
    $x = $a;
    $y = $b;
    $remainder = 0;
    while (($y != 0)) {
        $remainder = ($x % $y);
        $x = $y;
        $y = $remainder;
    }
    return alg_mul(intdiv($a, $x), $b);
}

$a = 12;
$b = 18;
$result = lcm($a, $b);
echo $result, PHP_EOL;