Find LCM and HCF of $13 x^{2} - 12 y^{2} a n d 6 x^{2} - 8 y^{2}$

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Solution

Given ,

$(13 x^{2} - 12 y^{2}), (6 x^{2} - 8 y^{2})$

$(13 x^{2} - 12 y^{2}), 2 (3 x^{2} - 4 y^{2})$

Hence HCF is $= 1$

And LCM is

$= (13 x^{2} - 12 y^{2}) \times 2 (3 x^{2} - 4 y^{2})$

$= 2 (13 x^{2} - 12 y^{2}) (3 x^{2} - 4 y^{2})$

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13 x^{2} - 12 y^{2} = 40; 6 x^{2} - 8 y^{2} = 16

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The LCM of the two numbers is $9$ times their HCF. The sum of LCM and HCF is $500.$ Find their HCF.

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