Question

Using prime factorization, find the HCF and LCM of

(i) $144,198$

Answer 1

Solution:

Step 1: Finding the prime factors:

$$\begin{gathered} 144=2^4\times 3^2 \\ 198=2\times 3^2\times 11 \end{gathered}$$

Step 2: Find LCM and HCF:

HCF is the product of each prime factor with lowest power. Therefore,

HCF($144,198$) $=2\times 3^2=18$

LCM is the product of each prime factor with highest power. Therefore,

LCM($144,198$) $=2^4\times 3^2\times 11=1584$

Final answer: Hence, HCF$\mathbf{=}\mathbf{18}$ and LCM$\mathbf{=}\mathbf{1584}$