Question

The L.C.M of $xy+yz+zx+y^2$ and $x^2+xy+yz+zx$ is

• A. $x+y$
• B. $y+z$
• C. $(x+y)(y+z)(z+x)$
• D. $x^2+y^2$

Answer 1

Answer: (C)

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

Consider $xy+yz+zx+y^2$ and factorise it as follows:

$xy+yz+zx+y^2=(xy+y^2)+(yz+zx)=y(x+y)+z(y+x)=(y+z)(x+y)$ ............(1)

Now consider $x^2+xy+yx+zx$ and factorise it as follows:

$x^2+xy+yz+zx=(x^2+xy)+(yz+zx)=x(x+y)+z(x+y)=(x+z)(x+y)$............(2)

Now, the least common multiple of equations 1 and 2 is $(x+y)(y+z)(z+x)$.

Hence, the L.C.M. of $xy+yz+zx+y^2$ and $x^2+xy+yz+zx$ is $(x+y)(y+z)(z+x)$.