Question

the least number by which 24 must be multipledto get a perfect cube is​

Answer 1

Cubes:-

$1^{3} =1$

$2^{3} =8$

$3^{3} =27$

$4^{3} =64$

$5^{3} =125$

$6^{3} =216$

$7^{3} =343$

$8^{3} =512\\9^{3} =729\\10^{3}=1000$

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Explanation :-

First we need to factorise 24

24 = 2 × 2 × 2 × 3

24 = 2³ × 3

To be a perfect cube, The number's Factors should be in form of triplets or cubes

24 = 2³ × 3

24 = 2 × 2 × 2 × 3

24 × 3 × 3 = 2 × 2 × 2 × 3 × 3 × 3

24 × 9 = 2³ × 3³

216 = 2³ × 3³

$\sqrt[3]{216} = \sqrt[3]{2^{3} * 3^{3} }$

in Right Hand Side ( RHS ) cubes and cube roots get cancelled

$\sqrt[3]{216} =$ 2 × 3

$\sqrt[3]{216}$ = 6

∴ The Least number that need to be multiplied to 24 is 9

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Hope It Helps You ! :D

By Abhiram5566

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