The sets $$A = \{z : z^{18} = 1\}$$ and $$B = \{w : w^{48} = 1\}$$ are both sets of complex roots of unity. The set $$C = \{zw : z \in A ~ \mbox{and} ~ w \in B\}$$ is also a set of complex roots of unity. How many distinct elements are in $$C^{}_{}$$?

(第八届AIME1990 第10题)