def _multiply_large_number_and_digit(number: str, digit: int) -> str:
    """Multiply a large number (as string) and a digit."""
    large_product = ''
    remainder = 0
    for num_digit in reversed(number):
        current_product_digit = remainder + int(num_digit) * digit
        large_product = str(current_product_digit % 10) + large_product
        remainder = current_product_digit // 10
    if remainder:
        large_product = str(remainder) + large_product
    return large_product