Question

Find the HCF of 105 and 1515 by prime factorisation method and hence find its LCM.

Answer 1

The given integers $105$ and $1515$ can be factorised as follows:

$105=3\times 5\times 71515=5\times 3\times 101$

$3,5,7$ and $101$ 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 $105$ and $1515$ is:

$HCF=3\times 5=15$

Also, the $LCM$ is the least common multiple, therefore, the $LCM$ of $105$ and $1515$ is:

$LCM=3\times 5\times 7\times 101=10605$

Hence, the $HCF$ is $15$ and $LCM$ is $10605$.