Find the $LCM$ and $HCF$ of $6$ and $20$ by the prime factorisation method.

(N/A) First,we find the prime factorisation of the given numbers:
$6 = 2^1 \times 3^1$
$20 = 2^2 \times 5^1$
To find the $HCF$,we take the product of the smallest power of each common prime factor:
$HCF(6, 20) = 2^1 = 2$
To find the $LCM$,we take the product of the greatest power of each prime factor involved in the numbers:
$LCM(6, 20) = 2^2 \times 3^1 \times 5^1 = 4 \times 3 \times 5 = 60$
Thus,the $HCF$ is $2$ and the $LCM$ is $60$.