Question

Find HCF and LCM of $336$ and $54$ by prime factorization and verify that?

Answer 1

Step1: Find the HCF and LCM

Factors of $336$ are :

$$\begin{gathered} 336=2\times 2\times 2\times 2\times 3\times 7 \\ 336=2^4\times 3\times 7 \end{gathered}$$

Factors of $54$ are :

$$\begin{gathered} 54=2\times 3\times 3\times 3 \\ 54=2\times 3^3 \end{gathered}$$

HCF of $(336,54)=2\times 3$

HCF of $(336,54)=6$

LCM of $(336,54)=2^4\times 3^3\times 7$

LCM of $(336,54)=3024$

Step 2: Verify the HCF and LCM

Multiples of HCF and LCM is equal to the product of two numbers.

HCF × LCM × HCF = Product of two numbers

$$\begin{gathered} 6\times 3024=336\times 54 \\ 18144=18144 \end{gathered}$$

Therefore LHS=RHS

Hence the HCF and LCM of $\left(336,54\right)$ are $6$ and $3024$ respectively and it is verified .