Question

Find the LCM of the following by prime factorisation method

$10,12,18$

Answer 1

Prime factorisation of $10$is

$10=2\times 5$

Prime factorisation of $12$ is

$12=2\times 2\times 3=2^2\times 3$

Prime factorisation of $18$ is

$18=2\times 3\times 3=2\times 3^2$

Here maximum number of times $2$ occurs $=2$

maximum number of times $3$ occurs $=2$

maximum number of times $5$ occurs $=1$

Therefore, $L.C.M=2^2\times 3^2\times 5=180$

Hence, LCM of $10,12,18$ by prime factorisation method is $180$.