Stacking and cutting identical wooden blocks

Identical wooden blocks are cuboids measuring \(18\text{ cm}\) by \(30\text{ cm}\) by \(45\text{ cm}\).

1. Blocks are stacked, all in the same orientation and with no gaps, to form a solid cube. Find the smallest possible side length of the cube and the number of blocks used.[3]
2. One block is cut into identical cubes with no wastage. Find the largest possible side length of each small cube and the number of small cubes obtained.[2]
3. Ken claims that if the blocks may be turned to different orientations, a solid cube of side \(60\text{ cm}\) can be built from whole blocks. Explain whether Ken is correct.[2]