"""
 divisible_by_1_to_n.py

 Ask for an integer n.
 Then find and print the first integer divisible by 1 through n.

 (The brute force method here is *not* an efficient way to solve this problem.)

 programing class exercise, Jim Mahoney | Oct 3 2011 | GPL
"""

def x_is_divisible_by_y(x, y):
    """ Return True if x is divisible by y.
        >>> x_is_divisible_by_y(10, 3)
        False
        >>> x_is_divisible_by_y(10, 5)
        True
    """
    return x % y == 0

def x_is_divisible_by_1_to_n(x, n):
    """ Return True if x is divisible by y.
        >>> x_is_divisible_by_y(10, 3)
        False
        >>> x_is_divisible_by_y(10, 5)
        True
    """
    for i in range(1, n+1):
        if not x_is_divisible_by_y(x, i):
            return False
    return True

def first_1_to_n_multiple(n):
    """ Return first integer divisible by 1 through n
        >>> first_1_to_n_multiple(3)
        6
        >>> first_1_to_n_multiple(10)
        2520
    """
    x = n
    while True:
        if x_is_divisible_by_1_to_n(x, n):
            return x
        x = x + 1

def main():
    n = input("What is n? (10) ")
    answer = first_1_to_n_multiple(n)
    print "%i is divisible by all the integers up to %i" % (answer, n)

if __name__ == "__main__":
    import doctest
    doctest.testmod()
    main()