Question

A rectangular block of length 20 cm, breadth 15 cm and height 10 cm is cut up into exact number of equal cubes the least possible number of cubes will be

Answer 1

Answer:

Answer is : 40

Step-by-step explanation:

As the block is in the shape of a cuboid with length(l)=20cm, breadth(b)=15cm and height(h)=10cm

Volume of the block = (6 x 12 x 15) cm^3 = 1080.  (as volume of cuboid=l×b×h)

 let the number of cubes=n

Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.

Volume of a cube = (3 x 3 x 3) = 27 cm^3.

volume of block=n×volume of a cube

Number of cubes(n)= 1080/27 = 40

hence, least possible number of cubes will be 40.

Answer 2

Answer:

24

Step-by-step explanation:

volume of block = l*b*h = 20 x 15 x 10 = 3000cm cube.

HCF of 20, 15, 10 === 5.

volume of cube = (HCF)^3 = 5^3 = 125 cm cube.

vol of block 3000

n== __________ = ______ = 24.

vol of cube 125

===>>>> Ans. - 24