Problem Statement
Find the HCF and LCM of $6, 72$ and $120$, using the prime factorization method.
Verified Solution & Marking Scheme
Prime Factorize Each Number
$$6 = 2^1 \times 3^1$$
$$72 = 2^3 \times 3^2$$
$$120 = 2^3 \times 3^1 \times 5^1$$
Calculate HCF
HCF is product of the smallest power of each common prime factor:
$$\text{HCF} = 2^1 \times 3^1 = 6$$
Calculate LCM
LCM is product of the greatest power of each prime factor involved:
$$\text{LCM} = 2^3 \times 3^2 \times 5^1 = 8 \times 9 \times 5 = 360$$