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Find the LCM of the following: $x^{2} y + x y^{2}, x^{2} + xy$

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xy (x + y)

xy (x - y)

{xy}^{2} (x + y)

None of these

answer is A.

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Detailed Solution

Given expression are,

x^{2} y + x y^{2},

x^{2} + xy

Now, the LCM = least common multiple in both expression.
First expression can be written as,

x^{2} y + x y^{2}

Take xy common,

x^{2} y + x y^{2}

= xy (x + y)

Second expression can be written as,

x^{2} + xy

Take x common,

x^{2} + xy = x (x + y)

Now multiply all the factors as,

x \times y \times (x + y) = xy (x + y)

Thus, the least common multiple (LCM) of

x^{2} y + x y^{2}

and

x^{2} + xy

xy (x + y) .

So, option 1 is correct.

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