Find the HCF and LCM of the following expressions:
$8x^4{a}^2,48y^2{b}^4$

The given monomials $8x^4{a}^2$ and $48x^2{b}^4$ can be factorised as follows:

$8x^4{a}^2=2\times 2\times 2\times x\times x\times x\times x\times a\times a48x^2{b}^4=2\times 2\times 2\times 2\times 3\times x\times x\times b\times b\times b\times b$

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $8x^4{a}^2$ and $48x^2{b}^4$ is:

$HCF=2\times 2\times 2\times x\times x=8x^2$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $8x^4{a}^2$ and $48x^2{b}^4$ is:

$LCM=2\times 2\times 2\times 2\times 3\times x\times x\times x\times x\times a\times a\times b\times b\times b\times b=48x^4{a}^2{b}^4$

Hence, the $HCF$ is $8x^2$ and $LCM$ is $48x^4{a}^2{b}^4$.