def worker(a, b):
    i, j, k = a, b, a
    while a != b:
        if a < b:
            a += i
        else:
            n = a - b
            k = n if not k else min(k, n)
            b += j

    return k, b / j + 1

>>> worker(4, 4)
(4, 2)
>>> worker(2, 3)
(1, 3)