Least Common Multiple in Python

from bisect import bisect_left

# Least Common Multiple in Python
#
# 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
# Python 3.9+: automatic lengths, native lists, arbitrary-precision arithmetic, and
# bisect_left for LIS. Invalid scalar/shape inputs raise ValueError. Integer element types
# and sorted/tree invariants remain caller preconditions.
#
# EXAMPLE
# Expected return: 36.
# Run: python example.py
# Tests for this exact source artifact run before publication. The accompanying source
# archive includes unit cases, runtime results, and source hashes.

def alg_require(condition):
    if not condition:
        raise ValueError("invalid algorithm input; see contract")
def alg_size(n):
    alg_require(0 <= n <= 4000000)
    return n

def lcm(a: int, b: int) -> int:
    alg_require(type(a) is int and -2147483648 <= a <= 2147483647)
    alg_require(type(b) is int and -2147483648 <= b <= 2147483647)
    alg_require(a >= 0 and b >= 0)
    if a == 0 or b == 0:
        return 0
    x: int = a
    y: int = b
    remainder: int = 0
    while y != 0:
        remainder = x % y
        x = y
        y = remainder
    return a // x * b

a = 12
b = 18
result = lcm(a, b)
print(result)