Question

What is the least number by which 30375 should be multiplied to get a perfect cube ?

Answer 1

3 is the least number by which 30375 should be multiplied to get a perfect cube.

Solution:

Prime Factors of 30375 are:

$\begin{array}{c | l} 3 & 30375 \\ \cline{2-2} 3 & 10125 \\ \cline{2-2} 3 & 3375 \\ \cline{2-2} 3 & 1125 \\ \cline{2-2} 3 & 375 \\ \cline{2-2} 5 & 125 \\ \cline{2-2} 5 & 25 \\ \cline{2-2} 5 & 5 \\ \cline{2-2} & 1\end{array}$

30375 = 3x3x3x3x3x5x5x5

=> (3x3x3) x (5x5x5) x 3 x 3

Clearly, we should multiply 30375 with 3 to get a perfect cube.

=> 30375 x 3 = 91125.

=> 91125 is a perfect cube of 45.

Hence, 3 is the least number by which 30375 should be multiplied to get a perfect cube.