Question

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

Answer 1

Solve for the H.C.F and L.C.M of the given numbers

The prime factors of $144=2\times 2\times 2\times 2\times 3\times 3$

The prime factors of $180=2\times 2\times 3\times 3\times 5$

The prime factors of $192=2\times 2\times 2\times 2\times 2\times 2\times 3$

$\therefore$LCM$(144,180,192)=2\times 2\times 2\times 2\times 2\times 2\times 3\times 3\times 5$

$\Rightarrow$L.C.M.$=2880$

$\therefore$ HCF$(144,180,192)=2\times 2\times 3$

$\Rightarrow$H.C.F.$=12.$

Hence, the HCF is$12$ and L.C.M is $2880$.