Question

$find \: the \: lcm \: of \: {x}^{2} - 4 \: and \: {x}^{2} - 16$

Answer 1

firstly find the factors of x^2 - 4 & x^2 - 16

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

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

no common factors are seen so LCM is product of given terms

i. e.

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

= ( x - 2 ) ( x + 2 ) ( x - 4 ) ( x + 4 )