Question

the LCM of n, 63, 81 is 1134 find 3 possible of n

Answer 1

$\large{\text{\underline{Note:-}}}$

Please check the question again. There are four values of $n$.

$\large{\text{\underline{To find:-}}}$

The four possible values of $n$, where the LCM of the three numbers is 1134.

$\large{\text{\underline{Let's begin:-}}}$

The LCM can be calculated in the following way.

• Choose the prime factors of the highest degree. Then, each factor is multiplied by the other. The result of the calculation is LCM.

The HCF can be calculated in the following way.

• Choose the prime factors of the lowest degree. Then, each factor is multiplied by the other. The result of the calculation is HCF.

$\large{\text{\underline{Solution:-}}}$

Prime factorization of two numbers

①$63=3^{2}\times 7$

②$81=3^{4}$

Firstly, the LCM of two known numbers is $3^{2}\times7=63$.

Prime factorization of the number

③$1134=2\times3^{4}\times7$

By the method of the LCM, the equation for $k$ is,

$\hookrightarrow 3^{2}\times 7\times k=2\times3^{4}\times7$

$\hookrightarrow k=2$

Let's find the LCM again.

As we are finding the LCM of $n$, 63, 81, the number $k$ can be multiplied by other factors. So, the following numbers are the possible values of $n$.

$\hookrightarrow k=2$

$\hookrightarrow 3\times k=6$

$\hookrightarrow 7\times k=14$

$\hookrightarrow 3^{2}\times k=18$

$\large{\text{\underline{Answer:-}}}$

Hence, the value of possible values of $n=2,6,14,18$.

This is the end of the required answer. Hope it helps.