The LCM of $x^{2} - 1,$ $x^{2} + 1$ and $x^{4} - 1$ is:

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

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

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

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None of these

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Solution

The correct option is A $(x^{2} + 1) (x^{2} - 1)$
First, we write all expressions as a product of their prime numbers.
So, $x^{2} - 1 = (x - 1) \times (x + 1)$
$x^{2} + 1 = 1 \times (x^{2} + 1)$
$x^{4} - 1 = (x - 1) \times (x + 1) \times (x^{2} + 1)$
We then choose each prime number with the greatest power and multiply them to get the LCM.
$=> L C M = (x - 1) \times (x + 1) \times (x^{2} + 1) = (x^{2} - 1) (x^{2} + 1)$

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