2. Use several $2 \times 3 \times 5$ small rectangular prisms to form a cube with an edge length of 90 by aligning them in the same direction. Then the number of small rectangular prisms that a diagonal of the cube passes through is ( ).
(A) 66
(B) 22
(C) 68
(D) 24
2. A.

Notice that, $[2,3,5]=30$, where $[x, y, z]$ represents the least common multiple of the positive integers $x, y, z$.

Therefore, we only need to find the number of small rectangular prisms a diagonal of a cube with edge length 30 passes through.
By the principle of inclusion-exclusion, we have
$$
\begin{array}{l}
\frac{30}{2}+\frac{30}{3}+\frac{30}{5}-\frac{30}{2 \times 3}-\frac{30}{2 \times 5}-\frac{30}{3 \times 5}+\frac{30}{2 \times 3 \times 5} \\
=22 .
\end{array}
$$

Thus, the answer is $22 \times 3=66$.
