Question

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

$510$ and$92$

Answer 1

Step 1: Find the prime factors and calculate the LCM and HCF of given numbers

The given integers are $510$ and $92$

First, let us find out the prime factors of $510$and $92$

The prime factors of $510=2\times 3\times 5\times 17$

The prime factors of $92=2\times 2\times 23$

$\Rightarrow$LCM$(510,92)=2\times 2\times 3\times 5\times 23\times 17$

$\Rightarrow$LCM$(510,92)=23460$

And, HCF$(510,92)=2$

Step 2: Compare with the product of H.C.F and L.C.M.

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

$$\begin{gathered} \Rightarrow 23460\times 2=510\times 92 \\ \Rightarrow 46920=46920 \end{gathered}$$

So, LHS=RHS

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

Hence, H.C.F.$(510,92)=2$ and L.C.M.$(510,92)=23460$

And, LCM$\times$HCF = the product of the integers $=46920$