Question

Find the LCM and HCF of the following integers by expressing them as product of primes $18,81$ and $108$.

Answer 1

The given integers $18$, $81$ and $108$ can be factorised as follows:

$18=2\times 3\times 381=3\times 3\times 3\times 3108=2\times 2\times 3\times 3\times 3$

$2$ and $3$ 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 $18$, $81$ and $108$ is:

$HCF=3\times 3=9$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $18$, $81$ and $108$ is:

$LCM=2\times 2\times 3\times 3\times 3\times 3=324$

Hence, the $HCF$ is $9$ and $LCM$ is $324$.