Question

If GCD of two numbers $a^2+b^2$ and $a+b$ is equal to 1, Then the LCM of these numbers is

• A. $a^2+b^2+a+b$
• B. $a^3+b^3+a+b$
• C. $a^2+b^2+ab(a+b)$
• D. $a^3+b^3+ab(a+b)$

Answer 1

The correct option is D $a^3+b^3+ab(a+b)$

$LCM\times HCF=\text{Product of the Numbers}$

Suppose A and B are two numbers, then.

$LCM(A,B)\times HCF(A,B)=A\times B$

From Question

$\Rightarrow 1\times LCM=\left(\begin{array}{c}{a}^2+b^2\end{array}\right)\times \left(\begin{array}{c}a+b\end{array}\right)$

$\Rightarrow LCM=a^3+b^3+a^{2}b+a{b}^2$

$\Rightarrow LCM=a^3+b^3+ab(a+b)$

Hence correct option is D.