Robin made a cuboid of plasticine. Length, breadth, and height of the cuboid are 3 cm, 2 cm, 3 cm respectively. How many such cuboids will he need to make a
perfect cube?

it's very easy

we know that a cube will have equal sides

that is if the length of one side is ‘A’

then its dimensions are A*A*A

now we need to make a cube using 3*3*5 cuboids

since from the dimensions of the cuboid we have two different numbers, they are 3 and 5

now we need to find a least number which is a multiple of both numbers, for this we can multiply thise numbers so that we can get the least number which is a multiple of those two

3*5=15

now imagine int the following way

1)keep one the 3*3 faces in front of you, now the side of length 5 is perpendicular to your body surface

2)now clone up this cuboid one upon one so that the resultant height becomes 15, since we are stacking cuboids of dimensions 3*3*5 one upon one keeping 3*3 on your face, the resultant height will be a multiple of 3

=>n(1)*3=15

=>n(1)=5

so u need to clone the cuboid vertically 5 times

3)now the resulting 3d figure will be of dimensions 15*3*5, we got one side equal to 15,

now we need to get the other two sides equal to 15

4)for the second side, keeping 15*3 face in front of you clone it horizontally in a direction away from you, if you do this the length 5 will increase in multiples of 5,clone it till u get it equal to 15

=>n(2)*5=15

=>n(2)=3

so you need to clone it 3 times in your opposite direction

5)now you will be left with a new 3d figure of dimensions 15*3*15,

now clone this whole set so that 3’s will add up to become 15,

=>n(3)*3=15

=>n(3)=5

you need to clone it 5 times in the horizontal plane in the other direction leaving your opposite direction

now you will get a cube of dimensions 15*15*15

6)now how many times you cloned a single cuboid is

=> n(1)*n(2)*n(3) = 5*3*5 = 15*3 = 75

so you need 75 cuboids to make a cube.