Using prime factorisation method, find HCF nad LCM of $36$ and $120$.

Represent $36$ and $120$ as a product of its prime factors.

prime factorization of $36=2\times 2\times 3\times 3$

prime factorization of $120=2\times 2\times 2\times 3\times 5$

HCF is the product of the lowest powers of each of the prime factors that commonly occurs in both the numbers,

LCM is the product of the maximum number of each prime factor that occurs in either of the numbers.

$$\begin{gathered} HCF=2^2\times 3=12 \\ LCM=2^3\times 3^2\times 5=360 \end{gathered}$$