Question

if the LCM of two numbers is 216 and their products is 7776, what will be the HCF​

Answer 1

$\frak{Given}\begin{cases}\sf{\:\:\: \: LCM \; of \; two \; numbers \; is \: \bf{216}}\\\sf{\;\;\; Product\;of\;two\: numbers\;is \: \bf{7776}}\end{cases}$

Need to find: HCF of both Numbers.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;\boxed{\sf{\purple{Product\;of\;two\; numbers= LCM \times HCF}}}$

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Therefore,

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• Product of Both Numbers is 7776.

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Now,

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$:\implies\sf 7776 = 216 \times HCF \\\\\\:\implies\sf HCF = \cancel\dfrac{7776}{216} \\\\\\:\implies{\underline{\boxed{\bf{\pink{HCF = 36}}}}}\;\bigstar$

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$\therefore\:{\underline{\sf{HCF \; of \; Both \:number\:is\: {\textsf{\textbf{36}}}.}}}$⠀

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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

Answer:

Given :-

• LCM of two numbers = 216
• Product = 7776

To Find :-

HCF

Solution :-

As we know that

HCF × LCM = Product of two numbers

Let the HCF be x

$\sf \: 216 \times x = 7776$

$\sf \: 216x = 7776$

$\sf \: x \: = \cancel\dfrac{7776}{216}$

$\sf \: x \: = 36$

HCF of two numbers are 36.

Know More :-

• HCF = Highest Common Factor
• LCM = Lowest Common Multiple