Question

The LCM of two numbers is 3456 and HCF is 48. If one of the numbers is 432, then what is the other number?​

Answer 1

$\huge \mathsf{\orange {\underline {\purple {\underline { Required \ answer \ ♡ \ :- }}}}}$

$\begin{gathered}\sf Given \begin{cases} & \sf{LCM\:of\:two\:numbers = \bf{3456}} \\ & \sf{HCF\:of\:two\:numbers = \bf{48}} \\ & \sf{One\:number\:is = \bf{432}} \end{cases}\\ \\\end{gathered}$

To find: Other number?

⠀⠀______________________________

☯ Let the other number be x.

⠀

$\begin{gathered}\dag\;{\underline{\frak{As\;we\;know\;that,}}}\\ \\\end{gathered}$

• The given natural numbers is equivalent to the product of the given numbers HCF and LCM The product of

⠀

$\begin{gathered}\star\;{\boxed{\sf{\pink{LCM \times HCF = Product\:of\:the\:numbers}}}}\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 3456 \times 48 = 432 \times x\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf 165888 = 432 \times x\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x = \cancel{ \dfrac{165888}{432}}\\ \\\end{gathered}$

$\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{x = 384}}}}}\;\bigstar\\ \\\end{gathered}$

Answer 2

Step-by-step explanation:

Given :-

LCM of two numbers=3456

HCF of two numbers=432

One no.=432

-->To find other number

let us suppose the other no.be x.

As we know that sum of natural no Equal to the product of equivalent numbers

HCF And LCM=Product of numbers

LCM×HCF=Product of numbers×x

===>3456×48=432× x

===>16588/432

===> x=384

then other no will be 384

hope it will help you dear