How to Find HCF and LCM

The factors of 8 are $1,2,4,8$, and the factors of 12 are $1,2,3,4,6,12$. The highest common factor is 4.

The multiples of 4 are $4,8,12,16$, and the multiples of 6 are $6,12,18$. The smallest multiple common to both is 12.

The multiples of 15 are $15,30,45,60$, and the multiples of 20 are $20,40,60$. The smallest common multiple is 60.

The factors of 45 are $1,3,5,9,15,45$, and the factors of 75 are $1,3,5,15,25,75$. The largest common factor is 15.

For 28, the prime factorisation is $2\times 2\times 7$. For 42, it is $2\times 3\times 7$. The LCM is $2\times 2\times 3\times 7=84$.

The prime factorisation of 72 is $2^3\times 3^2$, and the prime factorisation of 108 is $2^2\times 3^3$. Taking the highest powers of each prime gives $2^3\times 3^3=216$.