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

The other number = 384

Given :

• The LCM of two numbers is 3456 and HCF is 48

• One of the numbers is 432

To find :

The other number

Concept :

HCF :

For the given two or more numbers HCF is the greatest number that divides each of the numbers

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Relation between HCF and LCM :

HCF × LCM = Product of the numbers

Solution :

Step 1 of 2 :

Write down the given data

Here it is given that LCM of two numbers is 3456 and HCF is 48

One of the numbers is 432

Step 2 of 2 :

Find the other number

We know that ,

HCF × LCM = Product of the numbers

Thus we get ,

$\displaystyle \sf{ 48 \times 3456 = 432 \times Other \: number }$

$\displaystyle \sf{ \implies 432 \times Other \: number = 48 \times 3456 }$

$\displaystyle \sf{ \implies Other \: number = \frac{48 \times 3456}{432} }$

$\displaystyle \sf{ \implies Other \: number = 384 }$

Hence the other number = 384

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