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.
20
30
40
50
Explanation:
Volume of the block = (6 x 12 x 15) cm3 = 1080 cm3.
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.
Volume of this cube = (3 x 3 x 3) cm3 = 27 cm3.
Number of cubes = 1080/27 = 40.
Volume of the block = (6 x 12 x 15) cm3 = 1080 cm3.
Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm.
Volume of this cube = (3 x 3 x 3) cm3 = 27 cm3.
Number of cubes = 1080/27 = 40.