A rectanglar cuboid with dimensions 6 x12 x 15 is cut into

Question

A rectanglar cuboid with dimensions 6 x12 x 15 is cut into exact number of equal cubes . What will be the least number of cubes.

ssumitsh · Answer

2*4*5= 40 cubes.

size of each cbe = 3 X 3

Dan · Answer

Should be 6.

Total surface area = 684.

6s^2*n = 684, where n is the least number of cubes
s^2*n = 114

prime factorization of 114 = 6 * 19

(sqrt(19))^2 * 6 = 114

n = 6.

MA · Answer

cut the rectangular cubide solid with 3 x 3 x 3 size. if we cut the solid with these dimensions, there will be 40 cubes. this is the least number of equal cubes. more than this we can make 1x1x1 dimensions equal 1080 cubes as well.

neelesh · Answer

Side of each cube = n
Total number of cubes = k


6*12*15 = n^3 * k

k = 1080/n^3

Now all we need to do is have a max possible value of n that will result in a integer k.

n = 2, k = non integer 

n = 3, k = 40

n = 4, k = non integer

n = 5, k = non integer

n = 6 , k = non integer

n = 7 , k = non integer

n = 8, k = non integer

n = 9 , k = non integer

n > 9 , k < 1


Moreover the choices if there are any would drive the answer 

regards

Dan · Answer

maybe I am wrong, but we're interested in this question in the total surface area of the cuboid rather than in its volume since we want to 'cut' it rather than 'fill' it.

greenandwise · Answer

I get 5 cubes as the least number of cubes that you can get from a 6x12x15 rectangular cuboid:

Did the problem similar to neelesh:

k = 1080/n^3 = (6x12x15)/n^3 = (2*3*2*2*3*3*5)/n^3 = (6^3*5)/n^3 

when n = 6 k = 5...could be wrong though...whats the OA?

mein_aur_yeh_mba · Answer

Hi. I think it should be 40 cubes.

Since, we are looking at the least no. of same sized cubes, we are now looking for the max. volume of a cube that can be cut equally. 

Now looking at the dimension of cuboid : 6*12* 15 , the max. side that can be cut will be gcd of 6,12 and 15 which is 3. This implies that the max. side of the cube will be 3 with a max. volume of 27. 


Total volume of the cuboid = 1080

So the max. no. of cubes of the same side will be 1080/27 = 40

HSWKM · Answer

I think the answer is 5 cubes with a side of 6. 
( will explain if my answer is correct)

banerjeea_98 · Answer

5 cubes for me.

6x12x15 = nx^3 where n is number of cubes and x cube dimension.

2^3*3^3*5 = nx^3

For n to be least x3 has to be max....we get that for n = 5 and 

x^3 = 2^3*3^3


x===> 6

rxs0005 · Answer

Since we want to find out the least number of cubes then we should get the largest cube that can be made so highest common factor of the dimensions of 6 12 15 thats 3 so each cube will be volume 3^3 = 27

Total cubes = 6 * 12 * 15 / 27 = 40 

Answer = 40 cubes 

rxs0005

banerjeea_98 · Answer

Why is it not x(side) = 6, which will give you a lesser no of cubes i.e. 5 as I explained earlier ?

jinino · Answer

When n = 6, k=5. So the least number of cube is 5. 

rxs0005, is OA = 40?

vprabhala · Answer

i get it now. been understanding less number of cubes.. its the other way around.

jinino · Answer

The answer is not 5 cubes with each side = 6. Is that because for the side of 15, we cannot cut it to exact number? ie 15/6 is not an integer?

For the cubes with side = 3, each side can be divided into an integer. ie 6, 12, 15 /3 = 2, 4, 5

If so I would agree with the answer 40.

greenandwise · Answer

I still do not understand why 5 is not the answer. They are asking for the least number of cubes. If you divide 1080/6^3 you get 5, that is less thatn 40 and isn't that the question, the least number of cubes you can get? I think the OA is wrong!

HSWKM · Answer

The cube has to be cut exactly. I made a mistake in stating that 5 is the answer.

If the cube is of dimensions 6^3, you would get only 4 cubes and not 5 . The fifth one will be of dimensions 3*6*12. This is leftover, a cuboid, and so 4 as answer cannot satisfy the question's condition.

A rectanglar cuboid with dimensions 6 x12 x 15 is cut into

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