Algorithms: Number Theory

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

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);

    static int lcm(int a, int b) {
        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;

function power(int $base, int $exponent): int {
    alg_require(($exponent >= 0));
    $result = 1;
    while (($exponent > 0)) {
        if ((($exponent % 2) == 1)) {
            $result = alg_mul($result, $base);
        }
        $exponent = intdiv($exponent, 2);
        if (($exponent > 0)) {
            $base = alg_mul($base, $base);
        }
    }

    static int power(int base_value, int exponent) {
        checked {
            alg_require((exponent >= 0));
            int result = 1;
            while ((exponent > 0)) {
                if (((exponent % 2) == 1)) {
                    result = (result * base_value);
                }
                exponent = (exponent / 2);
                if ((exponent > 0)) {
                    base_value = (base_value * base_value);
                }