Question

Find the HCF and LCM of the following Expressions:
$10a^2{b}^2{c}^2,15a{b}^3{c}^2$ and $20b^3{c}^2$

Answer 1

The given monomials $10a^2{b}^2{c}^2$, $15a{b}^3{c}^2$ and $20b^3{c}^2$ can be factorised as follows:

$10a^2{b}^2{c}^2=2\times 5\times a\times a\times b\times b\times c\times c15a{b}^3{c}^2=3\times 5\times a\times b\times b\times b\times c\times c20b^3{c}^2=2\times 2\times 5\times b\times b\times b\times c\times c$

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $10a^2{b}^2{c}^2$, $15a{b}^3{c}^2$ and $20b^3{c}^2$ is:

$HCF=5\times b\times b\times c\times c=5b^2{c}^2$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $10a^2{b}^2{c}^2$, $15a{b}^3{c}^2$ and $20b^3{c}^2$ is:

$LCM=2\times 2\times 5\times 3\times a\times a\times b\times b\times b\times c\times c=60a^2{b}^3{c}^2$

Hence, the $HCF$ is $5b^2{c}^2$ and $LCM$ is $60a^2{b}^3{c}^2$.