Question 3: Find LCM of the following expressions by using prime factorization method:
\((v)\) \(\; \)\(16-4x^2,x^2+x-6,4-x^2 \)
Solution:
$\displaystyle 16-4x^{2} =4\left( 4-x^{2}\right)$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ =4\left( 2^{2} -x^{2}\right)$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ =4( 2-x)( 2+x)$
$\displaystyle x^{2} +x-6=x^{2} +3x-2x-6$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =x( x+3) -2( x+3)$
$\displaystyle \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ =-( x+3)( 2-x)$
$\displaystyle 4-x^{2} =2^{2} -x^{2}$
$\displaystyle \ \ \ \ \ \ \ \ \ \ =( 2-x)( 2+x)$
$\displaystyle \text{Common Factors} =( 2-x)( 2+x)$$\ =\ $$4-x^{2}$
$\displaystyle \text{Non-Common Factors} =-4( x+3)$
$\displaystyle \text{LCM}$$\ =\ $$\text{Common Factors} \times \text{Non Common Factors}$
$\displaystyle \text{LCM} =-4\left( 4-x^{2}\right)( x+3)$