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