By what least number should 4320 be multiplied so as to obtain a number which a perfect cube ?

Explanation:-

$$\eqalign{ & {\text{According to question}} \cr & \,\frac{{3\,\,\,|\,\,\,4320}}{{\frac{{3\,\,\,\,|\,\,\,\,1440}}{{\frac{{3\,\,\,\,|\,\,\,\,\,\,480}}{{\frac{{2\,\,\,\,|\,\,\,\,\,\,\,160}}{{\frac{{2\,\,\,\,|\,\,\,\,\,\,\,\,\,80}}{{\frac{{2\,\,\,\,|\,\,\,\,\,\,\,\,\,40}}{{\frac{{2\,\,\,\,|\,\,\,\,\,\,\,\,\,20}}{{\frac{{2\,\,\,\,|\,\,\,\,\,\,\,\,\,10}}{{\frac{{5\,\,\,\,|\,\,\,\,\,\,\,\,\,\,\,5}}{{\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,1}}}}}}}}}}}}}}}}}} \cr & {\text{Factors are}}\,\,:\, \cr & 3 \times 3 \times 3 \times 2 \times 2 \times 2 \times 2 \times 2 \times 5 \cr & \therefore {\text{It must be multiplied by,}} \cr & {\text{2}} \times {\text{5}} \times {\text{5 = 50}} \cr}$$