Question

The product of two numbers is 2662. If the LCM of these numbers is 242, find the their HCF

Answer 1

Answer:

We know, LCM x HCF = Product of two numbers

242 x HCF = 2662

HCF = 2662/242

HCF = 11

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Answer 2

Given:

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

To find:

• The HCF?

⠀⠀

Solution:

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

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

Verification:

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

⠀

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

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