A rectangular parallelepiped with edges 20, 24 and 32 needs to be folded from equal cubes.

| August 10, 2021 | education

A rectangular parallelepiped with edges 20, 24 and 32 needs to be folded from equal cubes. Find the largest possible volume of one such cube if you know that the length of the cube edge is an integer. Write down only the number in the answer.

First of all, from the very beginning, we should definitely pay attention to the point that, according to the condition of the given task, the cubes must be the same. This means that the largest cube satisfying the condition will have an edge equal to the greatest common divisor of the edges of the parallelepiped. Therefore, we get:
20 = 2 * 2 * 5;
24 = 2 * 2 * 2 * 3;
32 = 2 * 2 * 2 * 2 * 2.
Hence, GCD is equal to:
GCD (20, 24, 32) = 2 * 2 = 4.
This means that the volume of this cube is:
V = 4 ^ 3 = 4 * 4 * 4 = 64.
Answer: 64.



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