$The LCM of (x - 1)^{3} (x + 8) and (x - 1) (x + 8)^{2} is :$

(x - 1)^{3} (x + 8)^{2}

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(x - 1)^{3} (x + 8)^{3}

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(x - 1)^{2} (x + 8)^{2}

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(x - 1)^{2} (x + 8)^{3}

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Solution

The correct option is A $(x - 1)^{3} (x + 8)^{2}$
The common irreducible factors occuring in $(x - 1)^{3} (x + 8) a n d (x - 1) (x + 8)^{2}$ are $(x - 1) a n d (x + 8)$
The greatest exponents of these factors respectively are 3 and 2.
Hence, the LCM = $(x - 1)^{3} \times (x + 8)^{2} = (x - 1)^{3} (x + 8)^{2}$ .

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