Question

Find the $HCF$ and $LCM$ of $90$ and $144$ by the prime factorisation method.

Answer 1

Using the factor tree for the prime factorization of $90$ and $144$, we have
$90=2\times 3^2\times 5$ and $144=2^4\times 3^2$
To find the $HCF$, we list the common prime factor and their smallest exponents in $90$ and $144$ as under:
Common prime factor Least exponents
2 1
3 2
$\therefore$ $HCF=2^1\times 3^2=2\times 9=18$
To find the $LCM$, we list all prime factors of $90$ and $144$ and their greatest exponents as follows:
Prime factor of $90$ and $144$ Greatest exponents
2 4
3 2
5 1

$\therefore$ $LCF=2^4\times 3^2\times 5^1=16\times 9\times 5=720$