Lowest Common Multiple in Equations!

Algebra Level pending

Find the lowest common multiple of ( x 3 + 9 x 2 + 14 x x^{3}+9x^{2}+14x ) and ( 3 x 3 + 6 x 2 3x^{3}+6x^{2} ).

3 x ( x + 7 ) ( x + 3 ) 3x (x+7)(x+3) 3 x 2 ( x + 7 ) ( x + 2 ) 3x^{2} (x+7)(x+2) 3 x 3 ( x + 7 ) 2 ( x + 2 ) 3x^{3} (x+7)^{2}(x+2) 3 x 2 ( x + 7 ) ( x + 2 ) 2 3x^2 (x+7)(x+2)^{2}

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Jun 9, 2016

To find the LCM of x 3 + 9 x 2 + 14 x a n d 3 x 3 + 6 x 2 \large\color{#3D99F6}{x^{3}+9x^{2}+14x \ and\ 3x^{3}+6x^{2}} , we need to list the factors of each equation.

x 3 + 9 x 2 + 14 x = x ( x + 2 ) ( x + 7 ) \large x^{3}+9x^{2}+14x =\color{#3D99F6}{ x(x+2)}(x+7) ;

3 x 3 + 6 x 2 = 3 x x ( x + 2 ) \large 3x^{3}+6x^{2}= 3 x \color{#3D99F6}{x (x+2)} ⟹ the LCM is 3 x 2 ( x + 7 ) ( x + 2 ) \implies \text{ the LCM is} \boxed{\color{#3D99F6}{3x^{2}(x+7)(x+2)}}

Note: I colored the common factors between the two equations, so you take all the factors but for the repeated ones, you take only one of each factor, then multiply all the factors to get the LCM.

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