Find L.C.M and H.C.F of algebraic expressions $(x^{3} - 8)$ and $(x^{2} - 10 x + 16)$ .

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Solution

$x^{3} - 8 = (x - 2) (x^{2} + 2 x + 4)$
$x^{2} - 10 x + 16 = (x - 8) (x - 2)$
$⟹$ HCF $= (x - 2)$ and LCM $= (x - 2) (x - 8) (x^{2} + 2 x + 4)$

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