Question

Find the $HCF$ and $LCM$ of $144,180$ and $192$ by prime factorisation method.

Answer 1

Using the factor tree for the prime factorization of $144,180$ and $192$, we have

$144=2^4\times 3^2,180=2^2\times 3^2\times 5$ and $192=2^6\times 3$

To find the $HCF$, we list the common prime factor and their smallest exponents in $144,180$ and $192$ as follows:

Common prime factor Least exponents

2 2

3 1

$\therefore$ $HCF=2^2\times 3^1=12$

To find the $LCM$, we list all prime factors of $144,180,192$ and their greatest exponents as follows:

Prime factors of $144,180$ and $192$ Greatest exponents

2 6

3 2

5 1

$\therefore$ $LCM=2^6\times 3^2\times 5^1=64\times 9\times 5=2880$