Question

Find the HCF and LCM of the following Expression:
$p^5,p^{11},p^7$

Answer 1

The given monomials $p^5$, $p^{11}$ and $p^7$ can be factorised as follows:

$p^5=p\times p\times p\times p\times p{p}^{11}=p\times p\times p\times p\times p\times p\times p\times p\times p\times p\times p{p}^7=p\times p\times p\times p\times p\times p\times p$

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $p^5$, $p^{11}$ and $p^7$ is:

$HCF=p\times p\times p\times p\times p=p^5$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $p^5$, $p^{11}$ and $p^7$ is:

$LCM=p\times p\times p\times p\times p\times p\times p\times p\times p\times p\times p=p^{11}$

Hence, the $HCF$ is $p^5$ and $LCM$ is $p^{11}$.