If x = 103 then the LCM of $x^{2} - 4 a n d x^{2} - 5 x + 6$ is

105105

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1051050

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106050

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1060500

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Solution

The correct option is D 1060500
$x^{2} - 4 \Rightarrow (x)^{2} - (2)^{2}$
$\Rightarrow (x + 2) (x - 2)$
$x^{2} - 5 x + 6$
$\Rightarrow x^{2} - 3 x - 2 x + 6$
$\Rightarrow x (x - 3) - 2 (x - 3)$
$\Rightarrow (x - 3) (x - 2)$
$∴ L C M = (x + 2) (x - 2) (x - 3)$
Given $x = 103$
$L C M = (103 + 2) (103 - 2) (103 - 3)$
$\Rightarrow 105 \times 101 \times 100 \Rightarrow 1060500$

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A

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