Find the LCM of $a^{2} b + a b^{2}$ and $a^{3} + a^{2} b$ .

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Solution

The factors of the above expressions are: $a^{2} b + a b^{2} = a b (a + b)$ and $a^{3} + a^{2} b = a^{2} (a + b)$ . Here again we see that the highest power of $a$ is $a^{2}$ , that of $b$ is $b$ and that of $a + b$ is $a + b$ . Hence the LCM of these two expressions is $a^{2} b (a + b)$ .

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