If the HCF of the polynomials \( \left(x^{2}+8 x+16\right)\left(x^{2}\right. \) \( -9) \) and \(...

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If the HCF of the polynomials \( \left(x^{2}+8 x+16\right)\left(x^{2}\right. \) \( -9) \) and \( \left(x^{2}+7 x+12\right) \) is \( x^{2}+7 x+12 \), then their LCM is
(a) \( (x+4)\left(x^{2}-9\right) \)
(b) \( (x+4)^{2}\left(x^{2}-9\right) \)
(c) \( \left(x^{2}-4\right)\left(x^{2}+9\right) \)
(d) \( (x+4)^{2}(x+3) \)
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