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

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

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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Therefore,

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

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

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

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

$\Large\bold{\mathcal{\colorbox{yellow}{\blue{Solution:⤵}}}} \\ \large \bold{ \mathtt{ \colorbox{red}{ \blue{Given \: HCF=12,LCM=5040}}}} \\ \large \bold{ \mathcal{ \colorbox{pink}{ \pink{and also one number is 144}}}} \\ \large \bold{ \mathtt{ \colorbox{yellow}{ \blue{Let the other number be x}}}} \\ \large \bold { \mathtt{ \colorbox{orange}{{As we know that}}}} \\ \large \bold{ \mathtt{ \colorbox{navy}{ \orange{Product of two numbers is HCF×LCM}}}} \\ \large \bold{ \mathtt{ \colorbox{orange}{ \red{⟹144×x=12×5040}}}} \\ \large \bold{ \mathtt{ \colorbox{lime}{ \purple{⟹x=420}}}} \\ \large \bold{ \mathtt{ \colorbox{aqua}{ \red{So, The other number is 420}}}}$