Question

find the LCM of x2 - 4 and x4 - 16 with steps

Answer 1

hope you get it........

Answer 2

Answer:

The LCM of the numbers is $x^4-16$

Step-by-step explanation:

Given : Numbers $x^2-4$ and $x^4-16$

To find : The LCM of the numbers?

Solution :

First we factor the numbers,

$x^2-4=x^2-2^2$

$x^2-4=(x+2)(x-2)$ ....(1)

$x^4-16=(x^2)^2-(4)^2$

$x^4-16=(x^2-4)(x^2+4)$

$x^4-16=(x+2)(x-2)(x^2+4)$ .....(2)

The least common multiple of the numbers from (1) and (2) is

$LCM((x^2-4),(x^4-16))=(x+2)(x-2)(x^2+4)$

$LCM((x^2-4),(x^4-16))=x^4-16$

Therefore, The LCM of the numbers is $x^4-16$