  In this paper we use continued fractions to study a partial order on the set
of 2-bridge knots derived from the work of Ohtsuki, Riley, and Sakuma. We
establish necessary and sufficient conditions for any set of 2-bridge knots to
have an upper bound with respect to the partial order. Moreover, given any
2-bridge knot K we characterize all other 2-bridge knots J such that {K, J} has
an upper bound. As an application we answer a question of Suzuki, showing that
there is no upper bound for the set consisting of the trefoil and figure-eight
knots.
