Question

the product of two number is 2662 if the LCM of this number is 242 find their HCF ​

Answer 1

let the number be x and y.

$x \times y = lcm \times hcf$

x × y = 2662

lcm = 242

$2662 = 242 \times hcf$

$hcf = \frac{2662}{242}$

$hcf = 11$

therefore the HCF of the number is 11.

#answerwithquality

Answer 2

Given: 

• The product of the two numbers is 2662. & the LCM of these two given numbers is 242.

Need to find: 

• The HCF?

⠀⠀

Solution:

❍ Let's say, that the HCF of the two numbers be x.

$\begin{gathered} : \implies\sf\quad HCF \times LCM = Product_{\:(Numbers)}\\\\\\\end{gathered} \\ \\ \begin{gathered} :\implies\sf\quad x \times 242 = 2662\\\\\\\end{gathered} \\ \\ \begin{gathered} : \implies\sf\quad 242x = 2662\\\\\\\end{gathered} \\ \\ \begin{gathered} : \implies\sf\quad x = \cancel\dfrac{2662}{242}\\\\\\\end{gathered} \\ \\\begin{gathered} : \implies\quad\underline{\boxed{{\frak{{x = 11}}}}}\red\bigstar\\\\\end{gathered} \\ \\ \therefore{\underline{\textsf{Hence, the HCF of two numbers is \textbf{11}.}}}$

Verification:

• Now, Let's verify the answer by substituting the value of x as 11.

⠀

$\begin{gathered}\longmapsto\quad \boxed {\sf{ HCF \times LCM = Product_{\:(Numbers)}}}\\\\\\\end{gathered} \\ \begin{gathered}\longmapsto\sf\quad x \times 242 = 2662\\\\\\\end{gathered} \\ \begin{gathered}\longmapsto\sf\quad 11 \times 242 = 2662\\\\\\\end{gathered} \\ \begin{gathered}\longmapsto\quad\underline{\boxed{{\frak{2662=2662}}}} \blue\bigstar\\\\\end{gathered} \\\qquad\qquad\therefore{ \underline{\underline{\sf{{HENCE\; VERIFIED!}}}}}$

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||TheUnknownStar||