1. A wooden cuboid with edges $72 \mathrm{dm}, 96 \mathrm{dm}$ and $120 \mathrm{dm}$ is divided into equal cubes, with the largest possible edge, such that the edge length is a natural number. The resulting cubes are arranged one on top of another, forming a column. How many meters high is the resulting column?
Solution. The length of the edge of the cubic blocks is equal to $\mathrm{GCD}(72,96,120)=24 \mathrm{dm}$. According to this, the edges of the cuboid are divided into $72: 24=3, 96: 24=4$ and $120: 24=5$ parts, which means that the cuboid is divided into $3 \cdot 4 \cdot 5=60$ blocks. Finally, the height of the resulting column is equal to $60 \cdot 24=1440 \mathrm{dm}=144 \mathrm{~m}$.