A cuboid of dimensions 50 cm × 40 cm × 30 cm is cut into k cubes. What is the least possible value of k?

To find the least possible value of k, we need to find the volume of the smallest cube that can be cut from the cuboid.

Step 1: Find the greatest common divisor (GCD) of the dimensions of the cuboid. The GCD of 50 cm, 40 cm, and 30 cm is 10 cm. This means the smallest cube that can be cut from the cuboid is 10 cm × 10 cm × 10 cm.

Step 2: Calculate the volume of the cuboid and the smallest cube. The volume of the cuboid is 50 cm × 40 cm × 30 cm = 60,000 cubic cm. The volume of the smallest cube is 10 cm × 10 cm × 10 cm = 1,000 cubic cm.

Step 3: Divide the volume of the cuboid by the volume of the smallest cube to find the least possible value of k. So, k = 60,000 cubic cm / 1,000 cubic cm = 60.

Therefore, the least possible value of k is 60.