find lcm and hcf of x^​2​ -4 ,x⁴-16

Dear Student,

$$\begin{gathered} ApplyingEuclid\text{'}sdivisionlemmato\left(x^4-16\right)and\left(x^2-4\right), \\ {x}^4-16=\left(x^2-4\right)\left(x^2+4\right)+0 \\ Since,theremainderis0,HCF=\left(x^2-4\right) \\ Thus,LCM=\frac{\left(x^4-16\right)\left(x^2-4\right)}{\left(x^2-4\right)}=x^4-16 \end{gathered}$$