Question

Find the LCM and HCF of the following integers by expressing them as product of primes
$12,15$ and $30$.

Answer 1

The given integers $12$, $15$ and $30$ can be factorised as follows:

$12=2\times 2\times 315=3\times 530=2\times 3\times 5$

$2,3$ and $5$ are prime numbers as these are the numbers that are only divisible by themselves.

We know that $HCF$ is the highest common factor, therefore, the $HCF$ of $12$, $15$ and $30$ is:

$HCF=3$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $12$, $15$ and $30$ is:

$LCM=2\times 2\times 3\times 5=60$

Hence, the $HCF$ is $3$ and $LCM$ is $60$.