Question : The LCM of $x^2-8x + 15$ and $x^2-5x + 6$ is:
Option 1: $(x-2)(x-3)^2(x-5)$
Option 2: $(x + 5) (x + 2) (x + 3)$
Option 3: $(x + 5) (x - 2) (x - 3)$
Option 4: $(x - 5) (x - 2) (x - 3)$
Correct Answer: $(x - 5) (x - 2) (x - 3)$
Solution :
Given: The equations are $x^2- 8x + 15$ and $x^2- 5x + 6$.
LCM is the product of every prime factor that is present in the numbers to the greatest power.
The factors of $x^2-8x+15$ is given as,
$=x^2-3x-5x+15$
$=(x-3)-5(x-3)$
$=(x-3)(x-5)$
The factors of $x^2-5x+6$ is given as,
$=x^2-3x-2x+6$
$=(x-3)-2(x-3)$
$=(x-3)(x-2)$
LCM of $(x^2- 8x + 15$, $x^2- 5x + 6)=(x-5)(x-2)(x-3)$
Hence, the correct answer is $(x-5)(x-2)(x-3)$.
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