Question

3. 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

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

Need to find: The other number?

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❍ Let the other required number be x respectively.

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

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

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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

Answer:

$420$

Step-by-step explanation:

Solution:

Let the other number be x.

As we know that

★ Product of two numbers = (HCF)(LCM) ★

A/q

HCF = 12

LCM = 5040

One number = x

⟹ x × 144 = 12 × 5040

⟹ 144x = 60480

⟹ x = 60480/144

⟹ x = 420

Hence, the other number is x = 420

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★ Verification ★

➟ Product of two numbers = HCF × LCM

➟ 420 × 144 = 12 × 5040

➟ 60,480 = 60,480