Question

The least number by which 24 must be multiplied to get a perfect cube is ​

Answer 1

Answer:

Answer:

9 is the least number by which 24 must be multiplied to get a perfect cube.

Step by step explanation :-

To find :-

The least number.

Solution:

Given that,

Number = 24

Therefore,

Using prime factorization method,

\begin{gathered}\Large{ \begin{array}{c|c} \tt 2 & \sf{ 24} \\ \cline{1-2} \tt 2 & \sf { 12} \\ \cline{1-2} \tt 2 & \sf{ 6} \\ \cline{1-2} \tt 3 & \sf{ 3} \\ \cline{1-2} \tt & \sf{ 1 } \end{array}}\end{gathered}

2

\cline1−22

\cline1−22

\cline1−23

\cline1−2

​

24

12

6

3

1

​

​

Prime factorization of 24 = 2 × 2 × 2 × 3

24 = 2³ × 3

Here,

Two 3's are required to make 24 perfect cube.

3 × 3 = 9.

Hence, 9 is the least number by which 24 must be multiplied to get a perfect cube.

Verification:

24 × 9 = 216

216 is a perfect cube.

Hence, Verified!

Step-by-step explanation: