Question 1064112
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={{{highlight(72)}}} 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.