Question

Using Prime Factorisation Method, determine the LCM of the numbers in each of the following : $108,135,162$

Answer 1

To find the LCM of any Numbers, first we need to find the Prime Factors

$2$	$108$	$3$	$135$	$2$	$162$
$2$	$54$	$3$	$45$	$3$	$81$
$3$	$27$	$3$	$15$	$3$	$27$
$3$	$9$	$5$	$5$	$3$	$9$
$3$	$3$		$1$	$3$	$3$
	$1$				$1$
Prime factors of $108$ are $2\times 2\times 3\times 3\times 3$		Prime factors of $135$ are $3\times 3\times 3\times 5$		Prime factors of $162$ are $2\times 3\times 3\times 3\times 3$
$=2^2\times 3^3$		$=3^3\times 5$		$=2\times 3^4$

To find the LCM we take all the prime numbers that appear in prime factorisation of all the numbers, and then check for the highest power of those prime numbers, in the LCM we take the highest power of that prime number.

we have $2,3and5$ as different prime numbers and the highest power of $2$ is $2$, $3$ is $4$ and $5$ is $1$, so the LCM is $2\times 2\times 3\times 3\times 3\times 3\times 5=1620$

Hence the LCM is $1620$