If the HCF of $x^{3} - 343 a n d x^{2} - 9 x + 14 i s (x - 7),$ then find their LCM

(x - 7) (x - 2) \times (x^{2} + 7 x + 49)

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(x - 7) (x + 2) \times (x^{2} + 7 x + 49)

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(x + 7) (x - 2) \times (x^{2} + 7 x + 49)

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none of the above

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Solution

The correct option is A $(x - 7) (x - 2) \times (x^{2} + 7 x + 49)$
$x^{3} - 343 = x^{3} - {(7)}^{3} = (x - 7) (x^{2} + 7 x + 49) x^{2} - 9 x + 14 = x^{2} - 2 x - 7 (x - 2) = (x - 7) (x - 2)$ HCF of the polynomials $(x - 7) ∴$ Reqd. LCM= $= \frac{(x^{3} - 343) \times (x^{2} - 9 x + 14)}{H C F} = \frac{(x - 7) (x^{2} + 7 x + 49) \times (x - 7) (x - 2)}{(x - 7)} = (x - 7) (x - 2) \times (x^{2} + 7 x + 49)$

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