Question

the HCF and LCM of two numbers are 12 and 5040 , respectively . if one of the numbers is 144 , find the other number?​

Answer 1

Answer:

$\begin{lgathered}\frak{Given}\begin{cases}& \sf{HCF\;of\;two\; Numbers =\frak{12}} \\ &\sf{LCM\;of\;two\;numbers=\frak{5040}} \\ &\sf{One\;of \: the \: number\;is=\frak{144}}\end{cases}\end{lgathered}$

Need to find : The other number ?

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❍ Let the other required number be x respectively .

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

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$\bf{\star}\;\boxed{\textsf{\textbf{\pink{Product\;of\;two\; Numbers\;=\;LCM \times \: HCF}}}}$

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$\begin{lgathered}:\implies\sf x \times 144 = 12 \times 5040\\\\\\:\implies\sf x \times 144 = 60480 \\\\\\:\implies\sf x = \cancel\dfrac{60480}{144} \\\\\\:\implies{\underline{\boxed{\pink{\frak{x = 420}}}}}\;\bigstar\end{lgathered}$

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$\therefore{\underline{\textsf{Hence, the other required number is {\textbf{420.}}}}}$

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$\begin{lgathered}\qquad\quad\boxed{\underline{\underline{\pink{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}\\ \\\end{lgathered}$

HCF is ( Highest common factor ) which is the greatest factor b/w given any numbers .

LCM is ( Lowest common factor ) which is the least number and LCM is exactly divisible by two or more numbers .

Answer 2

$\begin{lgathered}\frak{Given}\begin{cases}& \sf{HCF\;of\;two\; Numbers =\frak{12}} \\ &\sf{LCM\;of\;two\;numbers=\frak{5040}} \\ &\sf{One\;of \: the \: number\;is=\frak{144}}\end{cases}\end{lgathered}$

Need to find : The other number ?

⠀⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

❍ Let the other required number be x respectively .

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$\underline{\bf{\dag} \:\mathfrak{As\;we\;know\: that\: :}}$

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⠀

$\bf{\star}\;\boxed{\textsf{\textbf{\red{Product\;of\;two\; Numbers\;=\;LCM \times \: HCF}}}}$

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$\begin{lgathered}:\implies\sf x \times 144 = 12 \times 5040\\\\\\:\implies\sf x \times 144 = 60480 \\\\\\:\implies\sf x = \cancel\dfrac{60480}{144} \\\\\\:\implies{\underline{\boxed{\blue{\frak{x = 420}}}}}\;\bigstar\end{lgathered}$

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$\therefore{\underline{\textsf{Hence, the other required number is {\textbf{420.}}}}}$

⠀⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━⠀

$\begin{lgathered}\qquad\quad\boxed{\underline{\underline{\orange{\bigstar \: \bf\:More\:to\:know\:\bigstar}}}}\\ \\\end{lgathered}$

HCF is ( Highest common factor ) which is the greatest factor b/w given any numbers .

LCM is ( Lowest common factor ) which is the least number and LCM is exactly divisible by two or more numbers.