Question

Find the $LCM$ and $HCF$ of the following integers by the prime factorization method:
$72$ and $108$.

Answer 1

$72$ and $108$
$72=2\ast 36$,
$=2\ast 2\ast 18$,
$=2\ast 2\ast 2\ast 9$,
$=2\ast 2\ast 2\ast 3\ast 3=2^3\ast 3^2$.
$108=2\ast 54$,
$=2\ast 2\ast 27$,
$=2\ast 2\ast 3\ast 9$,
$=2\ast 2\ast 3\ast 3\ast 3=2^2\ast 3^3$.
$\therefore$ HCF of $72$ and $108=3^2\ast 2^2=36$.
$\therefore$ LCM of $72$ and $108=2^3\ast 3^3=216$.