In the rectangular parallelepiped in the figure, the lengths of the segments EH, HG, and EG are consecutive integers. The height of the parallelepiped is 12. Find the volume of the parallelepiped.
https://cdn.artofproblemsolving.com/attachments/6/4/f74e7fed38c815bff5539613f76b0c4ca9171b.png geometry3D geometryparallelepipedVolume