Question

Find the L.C.M .OF x³-27,(x-3)andx²-9​

Answer 1

Answer:

LCM is (x+3)(x-3)($x^{2}$ + 3x +9)

Step-by-step explanation:

$x^{3} - 27\\= (x)^{3} - (3)^{3} \\= (x-3)(x^{2} + 3x + 9)$

By using Identity

x²-9​

= (x)² - (3)²

= (x+3)(x-3)

By Using Identity

So x³-27,(x-3) and x²-9​ Have common factor (x+3) and Other Factors $(x^{2} + 3x + 9) , (x-3)$

So LCM is $(x+3)(x-3)(x^{2} + 3x +9)$

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