Question

Find the LCM and HCF of the following integers by the prime factorization method:
$306$ and $657$.

Answer 1

$306$ and $657$
$306=2\ast 153$,
$=2\ast 3\ast 51$,
$=2\ast 3\ast 3\ast 17=2^1\ast 3^2\ast {17}^1$.
$657=3\ast 219$
$=3\ast 3\ast 73=3^2\ast {73}^1$.
$\therefore$ HCF of $306$ and $657=3^2=9$.
$\therefore$ LCM of $306$ and $657=2\ast 3^2\ast 17\ast 73=22338$.