Question

$x=7^2\times {13}^1\times {19}^3$. Which smallest number should be multiplied by $x$ to make it a perfect cube?

• A. $7$
• B. $13$
• C. $91$
• D. $1183$

Answer 1

The correct option is D $1183$

We can see $x$ is expressed in terms of its prime factors
To make $x$ a perfect cube we need to ensure the prime factors are raised to an exponent value which is a multiple of $3$.
In this case $x=7^2\times {13}^1\times {19}^3$.

Here, number of $7$'s is $2$, number of $13$'s is $1$ and number of $19$'s is $3$.

So we need to multiply another $7$ and ${13}^2$ to the factorization to make $x$ a perfect cube.

Hence, the smallest number by which $x$ must be multiplied to obtain a perfect cube is $7\times {13}^2=1183$.

Therefore, option $D$ is correct.