<s>[INST] Confused about finding LCM of three numbers I need to find the LCM of three numbers:


*

*$x^2-36$

*$2x^2-12x$

*$x^2-6x$


I factor:


*

*$x^2-36=(x+6)(x-6)$

*$2x^2-12x=2x(x-6)$

*$x^2-6x=x(x-6)$


Then I multiply all factors. Every factor that appears in all three expressions I multiply only once. $(2x)(x)(x-6)(x+6)$. And I get $2x^2(x+6)(x-6)$. But the solution is $2x(x+6)(x-6)$. Where I'm wrong?
 [/INST] Note that $x$ is already contained in $2x$ thus $2\cdot x\cdot (x+6)\cdot (x-6)$ is the correct answer.
Indeed the different factors which appear are


*

*$2$

*$x$

*$(x-6)$

*$(x+6)$

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