Question

Find LCM and HCF of $510$ and $92$?

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

Answer 1

Step 1: Find the LCM and HCF of $510$ and $92$

$$\begin{gathered} 510=2\times 5\times 3\times 17 \\ 92=2\times 2\times 23 \end{gathered}$$

$\therefore HCF(510,92)=2$

L.C.M.$(510,92)=2\times 2\times 3\times 5\times 17\times 23$

$\Rightarrow$L.C.M.$(510,92)=23460$

Step 2: Verify that the product of two numbers is equal to the product of LCM and HCF.

Find the product of L.C.M and H.C.F.

$$\begin{gathered} LCM\times HCF=23460\times 2 \\ \Rightarrow =46920 \end{gathered}$$

Find the product of the given numbers.

$510\times 92=46920$

Since, $\text{L.C.M × H.C.F}=510\times 92$

Hence, it is verified that the product of LCM and HCF is equal to the product of two numbers.

The LCM of $510$ and $92$is $23,460$

The HCF of $510$ and $92$ is $2$

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