Question

Find the HCF and LCM of $4x^3,y^3,z^3$

Answer 1

The given monomials $4x^3$, $y^3$ and $z^3$ can be factorised as follows:

$4x^3=2\times 2\times x\times x\times x{y}^3=y\times y\times y{z}^3=z\times z\times z$

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $4x^3$, $y^3$ and $z^3$ is:

$HCF=1$ (There is no common factor between the given monomials)

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $4x^3$, $y^3$ and $z^3$ is:

$LCM=2\times 2\times x\times x\times x\times y\times y\times y\times z\times z\times z=4x^3{y}^3{z}^3$

Hence, the $HCF$ is $1$ and $LCM$ is $4x^3{y}^3{z}^3$.