A) Find the prime factorisation of 30 and 36. b) Hence, find the HCF and LCM of 30 and 36.

To find the HCF, take the lowest power of each common prime factor.
Common prime factors are 2 and 3.
Lowest power of 2: $2^1$
Lowest power of 3: $3^1$

$$\text{HCF}(30, 36) = 2^1 \times 3^1 = 2 \times 3 = 6$$

To find the LCM, take the highest power of all prime factors present in either number.
Highest power of 2: $2^2$
Highest power of 3: $3^2$
Highest power of 5: $5^1$

$$\text{LCM}(30, 36) = 2^2 \times 3^2 \times 5^1 = 4 \times 9 \times 5 = 36 \times 5 = 180$$

The HCF of 30 and 36 is $\boxed{6}$ and the LCM is $\boxed{180}$.