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A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact num

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Aakash0101raj
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A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact num [#permalink] New post   14 Nov 2022, 19:59
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A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes?

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Carcass
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Re: A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact num [#permalink] New post   15 Nov 2022, 00:05
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Volume of the block is 6*12*15=1080

HCF is among those three measures is 3 (find the greatest common division) to find the small cube

Volume of this cube is 3^3=27

The number of cubes possible is the largest or total volume by the small volume

1080/27=40
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rainer85
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Re: A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact num [#permalink] New post   04 Dec 2022, 17:18
Carcass wrote:
Volume of the block is 6*12*15=1080

HCF is among those three measures is 3 (find the greatest common division) to find the small cube

Volume of this cube is 3^3=27

The number of cubes possible is the largest or total volume by the small volume

1080/27=40


Why can't you use a cube with a volume of 1?
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r1smith
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Re: A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact num [#permalink] New post   09 Dec 2022, 15:04
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rainer85 wrote:
Why can't you use a cube with a volume of 1?


We are looking for the least number of cubes. That is why we are finding the HCF/GCF because that is the largest number each of the dimensions of the block can be divided by:

(6/3) x (12/3) x (15/3) = 2 x 4 x 5 = 40

If we chose to cut the block into cubes with a volume of 1, we'd have:

(6/1) x (12/1) x (15/1) = 1080

That's a lot of cubes and we are looking for the fewest amount of cubes.

Hope this helps clarify things.
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cristalplume
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Re: A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact num [#permalink] New post   08 Jul 2023, 02:50
r1smith wrote:
rainer85 wrote:
Why can't you use a cube with a volume of 1?


We are looking for the least number of cubes. That is why we are finding the HCF/GCF because that is the largest number each of the dimensions of the block can be divided by:

(6/3) x (12/3) x (15/3) = 2 x 4 x 5 = 40

If we chose to cut the block into cubes with a volume of 1, we'd have:

(6/1) x (12/1) x (15/1) = 1080

That's a lot of cubes and we are looking for the fewest amount of cubes.

Hope this helps clarify things.


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