Find the HCF and the LCM of 132 and 198 from their prime factorisations…

Step 1. Factorise. $132 = 2^2 \times 3 \times 11$ and $198 = 2 \times 3^2 \times 11$.

Step 2. HCF. Smaller powers: $2 \times 3 \times 11 = 66$.

Step 3. LCM. Greater powers: $2^2 \times 3^2 \times 11 = 396$.

Step 4. Check. $66 \times 396 = 26\,136$ and $132 \times 198 = 26\,136$.