The L.C.M. of $x y + y z + z x + y^{2}$ and $x^{2} + x y + y z + z x$ is

x + y

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y + z

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(x + y) (y + z) (z + x)

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x^{2} + y^{2}

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Solution

The correct option is C $x + y$
On factorising the given expressions we get, $x y + y z + z x + y^{2}$
= $y z + x y + x z + y^{2}$
= $z (y + x) + y (x + y)$
= $(x + y) (z + y)$
Also, $x^{2} - x y + y z + z x$
= $x (x + y) + z (y + x)$
= $(y + x) (x + z)$
Now, LCM or the common factor of $(x + y) (z + y)$ and $(y + x) (x + z) = (x + y)$

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