6. Several rectangular prisms with edge lengths of $2, 7, 13$ are assembled in the same orientation to form a cube with an edge length of 2002. The number of small rectangular prisms that a diagonal of the cube passes through is ( ).
A. 1190
B. 1200
C. 1170
D. 1210
6. D
The least common multiple of $2, 7, 13$ is 182, consider a cube with edge length 182. Using the principle of inclusion-exclusion, we have
$$
\frac{182}{2}+\frac{182}{7}+\frac{182}{13}-\frac{182}{2 \times 7}-\frac{182}{2 \times 13}-\frac{182}{7 \times 13}+\frac{182}{2 \times 7 \times 13}=110
$$

Therefore, the diagonal passes through $110 \times 11=1210$ small rectangular prisms.