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

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

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

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

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

• 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

Given :-

HCF of two numbers = 12

LCM of two number = 5040

One number = 144

To Find :-

Other number

Solution :-

We know that

$\star {\boxed{\frak{LCM \times HCF = Product \: of \: two \: numbers}}}$

Let the other number be b

$\tt \implies 12 \times 5040 = 144 \times b$

$\tt \implies 60480 = 144b$

$\tt \implies \dfrac{60480}{144} = b$

${\textsf{\textbf{\pink{\underline{Other number = 420}}}}}$