  We define the regular Euclidean algorithm and the general form which leads to
the method of least absolute remainders and also the method of negative
remainders. We are going to show that if looked from the perspective of
subtraction, the method of least absolute remainders and the regular method
have the same number of steps which is in fact the minimal number of steps
possible. This enables us to apply the theory in rational tangles to determine
the most efficient way to untangle a rational tangle.
