By what least number should 324 be multiplied to get a perfect cube?

Given :

The given number is 324

To find :

We have To find the  least number by which 324 should be multiplied to get a perfect cube

Solution :

Prime factorisation of 324 is,

324 = $2\times2\times3\times3\times3\times3 = (2\times2)\times(3\times3\times3)\times3$

Therefore, the given number to be a perfect cube should be multiplied by

$2\times3\times3=18$.

$324\times2\times3\times3 =  (2\times2)\times(3\times3\times3)\times3\times2\times3\times3$

       $324\times18 = (2\times2\times2)\times(3\times3\times3)\times(3\times3\times3)$

        $\displaystyle 5832\ =\ 2^{3} \times 3^{3} \times 3^{3}$

                    5832  = $(2\times3\times3)^{3}$

                      5832 = 18³ 

The  least number To be multiplied with 324 is 18 

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Updated on: 10-Oct-2022

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