Question

Find the LCM of x³-27, (x-3)², x²-9

Answer 1

Answer:

(x-3)² is the LCM of this question

Answer 2

LCM x³ - 27 , (x - 3)² , x² - 9 = (x + 3)(x - 3)²( x² + 3x + 9 )

Given :

The expressions x³ - 27 , (x - 3)² , x² - 9

To find :

The LCM

Solution :

Step 1 of 3 :

Write down the given expressions

The given expressions are

x³ - 27 , (x - 3)² , x² - 9

Step 2 of 3 :

Factorise the expressions

First expression

= x³ - 27

= x³ - 3³

= ( x - 3 ) ( x² + 3x + 9 )

Second expression

= (x - 3)²

= ( x - 3 ) ( x - 3 )

Third expression

= x² - 9

= x² - 3²

= ( x + 3 ) ( x - 3 )

Step 3 of 3 :

Find the LCM

The required LCM

= ( x + 3 )( x - 3 )( x - 3 )( x² + 3x + 9 )

= (x + 3)(x - 3)²( x² + 3x + 9 )

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