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.

Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm 

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) cu.cm = 27 cu.cm 

Number of cubes = $\frac{1080}{27}$ = 40.