Question

Find the HCF and LCM of $24a^5{b}^5{c}^4,30a^3{b}^4{c}^3,36a^2{b}^3{c}^5$

Answer 1

The given monomials $24a^5{b}^5{c}^4$, $30a^3{b}^4{c}^3$ and $36a^2{b}^3{c}^5$ can be factorised as follows:

$24a^5{b}^5{c}^4=2\times 2\times 2\times 3\times a\times a\times a\times a\times a\times b\times b\times b\times b\times b\times c\times c\times c\times c$

$30a^3{b}^4{c}^3=2\times 3\times 5\times a\times a\times a\times b\times b\times b\times b\times c\times c\times c$

$36a^2{b}^3{c}^5=2\times 2\times 3\times 3\times a\times a\times b\times b\times b\times c\times c\times c\times c\times c$

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $24a^5{b}^5{c}^4$, $30a^3{b}^4{c}^3$ and $36a^2{b}^3{c}^5$ is:

$HCF=2\times 3\times a\times a\times b\times b\times b\times c\times c\times c=6a^2{b}^3{c}^3$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $24a^5{b}^5{c}^4$, $30a^3{b}^4{c}^3$ and $36a^2{b}^3{c}^5$ is:

$LCM=2\times 2\times 2\times 3\times 3\times 5\times a\times a\times a\times a\times a\times b\times b\times b\times b\times b\times c\times c\times c\times c\times c=360a^5{b}^5{c}^5$

Hence, the $HCF$ is $6a^2{b}^3{c}^3$ and $LCM$ is $360a^5{b}^5{c}^5$.