Identical cubes

From the smallest number of identical cubes whose edge length is expressed by a natural number, can we build a block with dimensions 12dm x 16dm x 20dm?

Correct result:

n =  60

Solution:

a=12 dm b=16 dm c=20 dm  12=22⋅3 16=24 20=22⋅5 GCD(12,16,20)=22=4  x=GCD(a,b,c)=GCD(12,16,20)=4 dm  V1=a⋅ b⋅ c=12⋅ 16⋅ 20=3840 dm3 V2=x3=43=64 dm3  n=V1/V2=3840/64=60

Try another example


We would be pleased if you find an error in the word problem, spelling mistakes, or inaccuracies and send it to us. Thank you!






Showing 0 comments:
avatar




Tips to related online calculators
Do you want to calculate greatest common divisor two or more numbers?
Do you want to convert length units?
Tip: Our volume units converter will help you with the conversion of volume units.

You need to know the following knowledge to solve this word math problem:


 
We encourage you to watch this tutorial video on this math problem: video1

Next similar math problems:

  • The wooden
    cubes3 The wooden block measures 12 cm, 24 cm, and 30 cm. Peter wants to cut it into several identical cubes. At least how many cubes can he get?
  • Largest squares
    metals How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?
  • Cubes into cuboid
    cubes_21 How many 12 centimeter cubes fit into the block (cuboid) with 6dm, 8.4dm, and 4.8?
  • Aquarium
    akvarko_20 Can 30 liters of water fit in a cuboid aquarium with dimensions a = 3dm b = 6dm c = 5dm?
  • Tiles
    kachlicky Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
  • Water block
    cukr_8 A block with a 50 cm2 base is filled with water 5 cm under the edge. How many can sugar cubes with 2 cm edge be thrown into a container that overflow water?
  • Cubes
    krychlicky Carol with cut bar 12 cm x 12 cm x 135 cm to the cubes. Find the sum of all the surfaces of the resulting cubes.
  • The cube
    cubes_28 The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?
  • Sports students
    numbers_39 There are 120 athletes, 48 volleyball players, and 72 handball players at the school with extended sports training. Is it possible to divide sports students into groups so that the number in each group is the same and expressed by the largest possible num
  • Decompose
    cinema_5 Decompose into primes and find the smallest common multiple n of (16,20) and the largest common divisor D of the pair of numbers (140,100)
  • Swimming pool
    bazen_1 The swimming pool has the shape of a block with dimensions of 70dm, 25m, 200cm. How many hl of water can fit into the pool?
  • An example
    cubes3_2 An example is playfully for grade 6 from Math and I don't know how to explain it to my daughter when I don't want to use the calculator to calculate the cube root. Thus: A cuboid was made from a block of 16x18x48 mm of modeline. What will be the edge of t
  • Common divisors
    prime Find all common divisors of numbers 30 and 45.
  • Third dimension
    star_1 Calculate the third dimension of the cuboid: a) V = 224 m3, a = 7 m, b = 4 m b) V = 216 dm3, a = 9 dm, c = 4 dm
  • Segments
    segments Line segments 62 cm and 2.2 dm long we divide into equal parts which lengths in centimeters is expressed integer. How many ways can we divide?
  • Cube V2S
    cube_shield The volume of the cube is 27 dm cubic. Calculate the surface of the cube.
  • Groups
    children2_1 In the 6th class there are 60 girls and 72 boys. We want to divide them into groups so that the number of girls and boys is the same. How many groups can you create? How many girls will be in the group?