Find the LCM.
-$$\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }$$
A) $81 \mathrm { n } ^ { 2 }$
B) $n ^ { 2 } + 81$
C) $n + 9$
D) $n ( 9 + n ) ( 9 - n )$

Question

Quizplus · Accepted Answer

The LCM can be calculated by multiplying the greatest power of each prime factor that appears in the given numbers. Here, the prime factors are $n$, $3$, and $3-n$ (which is equal to $-(n-3)$). The greatest power of $n$ that appears is $n$, the greatest power of $3$ that appears is $3^2=9$, and the greatest power of $3-n$ that appears is $3-n$. Therefore, the LCM is $n \cdot 9 \cdot (3-n)=n(9+n)(9-n)$. Choice $\boxed{	extbf{(D)}}$ is the correct answer.

Find the LCM n,9+n,9−n\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }n,9+n,9−n

Find the LCM $\mathrm { n } , 9 + \mathrm { n } , 9 - \mathrm { n }$