Question

Find the HCF and LCM of the given monomials:
$9x^2{y}^2{z}^3,15x^3{y}^2{z}^4$

Answer 1

The given monomials $9x^2{y}^2{z}^3$ and $15x^3{y}^2{z}^4$ can be factorised as follows:

$9x^2{y}^2{z}^3=3\times 3\times x\times x\times y\times y\times z\times z\times z15x^3{y}^2{z}^4=3\times 5\times x\times x\times x\times y\times y\times z\times z\times z\times z$

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $9x^2{y}^2{z}^3$ and $15x^3{y}^2{z}^4$ is:

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

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $9x^2{y}^2{z}^3$ and $15x^3{y}^2{z}^4$ is:

$LCM=3\times 3\times 5\times x\times x\times x\times y\times y\times z\times z\times z\times z=45x^3{y}^2{z}^4$

Hence, the $HCF$ is $3x^2{y}^2{z}^3$ and $LCM$ is $45x^3{y}^2{z}^4$.