Question

Find the HCF of xy^2 , x^2y^3 , x^3y^3 and then find their LCM .

Answer 1

$\textbf{Given:}$

$xy^2,\;x^2y^2,\;x^3y^3$

$\textbf{To find:}$

$\text{HCF and LCM}$

$\textbf{Solution:}$

$\text{We find H.C.F and L.C.M by factorization method}$

$xy^2=\boxed{x}{\times}\boxed{y{\times}y}$

$x^2y^3=\boxed{x}{\times}x{\times}y{\times}\boxed{y{\times}y}$

$x^3y^3=\boxed{x}{\times}x{\times}x{\times}y{\times}\boxed{y{\times}y}$

$\text{Clearly xy^2 is a common factor of these 3 polynomials}$

$\therefore\bf\,H.C.F=xy^2$

$xy^2=x{\times}y^2$

$x^2y^3=x^2{\times}y^3$

$x^3y^3=x^3{\times}y^3$

$\text{Choose the highest power of each factors}$

$\therefore\bf\text{L.C.M= \bf\,x^3y^3 }$

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