SOLUTION: Mia has many rectangular blocks, each measuring 4cm by 3cm by 2cm. The number of blocks she must use to make the smallest possible cube is what?

Question 1064112: Mia has many rectangular blocks, each measuring 4cm by 3cm by 2cm. The number of blocks she must use to make the smallest possible cube is what?
Found 2 solutions by Theo, KMST:
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the rectangular blocks measures 4 by 3 by 2.

if she wants to make a cube, then each side of the cube has to be the same measure.

the least common multiple of 4 and 3 and 2 is 12.

4 * 3 = 12
3 * 4 = 12
2 * 6 = 12

assuming the height is 4 and the length is 3 and the depth is 2, they you get:

3 rectangles to form the height.
4 rectangles to form the length.
6 rectangles to form the width.

the number of rectangular blocks required would be 3 * 4 * 6 = 48.

each side of the cube would measure 12 cm.

it's very difficult to visualize, but i believe this is your answer.

Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
If she must use whole blocks,
the length b(in cm) of thredges of the cube must be
a multiple of 2, 3, and 4.
The smallest such multiple is 3�4=12=2�6.
A cube with edges measuring 12 cm
will require 3�4�6= blocks.
How do I calculate that?
The 4 cm edge of a block fits exactly
(12 cm) � (4 cm) = 3 times into a 12 cm edge of the cube.
The 3 cm block edge fits (12 cm) � (3 cm) = 4 times
into an adjacent cube edge.
A 2 cm block edge fits (12 cm) � (2 cm) = 6 times
into a third adjacent cube edge.
Mia could make 3-block by 4-block square wall
as the front face of the cube,
using 3�4=12 blocks.
Adding another 5 such squares behind the front face,
she would have a 3-block by 4-block by 6-block cube,
made using 3�4�6=72 blocks.

ANOTHER WAY:
A cube with edges measuring 12 cm has a volume of
(12 cm)�(12 cm)�(12 cm)=1,728 cubic cm.
A block measuring 4 cm by 3 cm by 2 cm has a volume of
(4 cm)�(3 cm)�(2 cm)=24 cubic cm.
(1,728 cubic cm) � (24 cubic cm per block) = 72 blocks.

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