$2 \cdot 8$ set $A=\left\{z \mid z^{18}=1\right\}, B=\left\{w \mid w^{48}=1\right\}$ are both sets of complex roots of unity, $C=\{z w \mid z \in A, w \in B\}$ is also a set of complex roots of unity, how many elements does set $C$ contain?