7. A rectangular prism of size $150 \times 324 \times 375$ is composed of $1 \times 1 \times 1$ unit cubes. The diagonal of this rectangular prism passes through $\qquad$ unit cubes.
Divide the cuboid using planes parallel to its faces. 150 parallel planes spaced 1 unit apart from left to right intersect the diagonal at 150 points, 324 parallel planes spaced 1 unit apart from front to back intersect the diagonal at 324 points, and 375 parallel planes spaced 1 unit apart from bottom to top intersect the diagonal at 375 points. Excluding the same points, there are a total of \(150 + 324 + 375 - (150, 324) - (150, 375) - (324, 375) + (150, 324, 375) = 849 - 6 - 75 - 3 + 3 = 768\) different points (including the right endpoint, excluding the left endpoint). These points divide the diagonal into 768 segments, each segment lying within a unit cube. Therefore, the diagonal of the cuboid passes through 768 unit cubes.