Question

Find the LCM and HCF of the following pairs of integers and verify that LCM$\times$HCF$=$ the product of the two numbers.

$336$and $54$

Answer 1

Step 1: Solve for the prime factors to calculate HCF and LCM of given numbers

The given integers are$336$ and$54$

Firstly, let us find out the prime factors for $336$ and $54$

The prime factors of $336=2\times 2\times 2\times 2\times 3\times 7$

The prime factors of $54=2\times 3\times 3x3$

$\Rightarrow$L.C.M. $(336,54)=2\times 2\times 2\times 2\times 3\times 3\times 3\times 7$

$\Rightarrow$L.C.M.$(336,54)=3024$

And,

$\Rightarrow$H.C.F.$(336,54)=2x3$

$\Rightarrow$H.C.F.$(336,54)=6$

Step 2: Compare the product of H.C.F and L.C.M. and that of given numbers

To check, L.C.M.$\times$H.C.F $=$ the product of two numbers.

$$\begin{gathered} \Rightarrow 3024x6=336\times 54 \\ \Rightarrow 18144=18144 \end{gathered}$$

So, LHS $=$RHS

$\therefore$LCM$\times$HCF = Product of the integers

Hence verified.

Hence, HCF$(336,54)=6$ and LCM$(336,54)=3024$

And, LCM$\times$HCF = product of the integers $=18144$.