A rectangular parallelepiped with a length of 35 cm, a width of 14 cm and a height of 21 cm

A rectangular parallelepiped with a length of 35 cm, a width of 14 cm and a height of 21 cm was cut into the same largest cubes. How many cubes did you get?

To find the side of the largest possible cube in a given rectangular parallelepiped, you need to find the greatest common divisor of all three sides. To do this, we factor each length:

35 = 5 * 7;

14 = 2 * 7;

21 = 3 * 7.

We see that the GCD is 7 cm, this will be the side of the desired cube.

Let’s find the volume of the parallelepiped:

V1 = 35 * 14 * 21 = 10290 cm³.

Let’s find the volume of each of the obtained cubes:

V2 = 7³ = 343 cm³.

To find how many cubes you get, let’s divide the total volume of the parallelepiped by the volume of the cube:

10290/343 = 30 cubes.

Answer: it turned out 30 cubes.