Math, asked by aman7272, 1 year ago

 

The LCM and product of two numbers is 72 and 864 respectively. Find their HCF.

Answers

Answered by Anonymous
44

We know that,

\boxed{\sf{LCM\:×\:HCF = Product\:of\:two\:numbers}}

Let the two numbers be a and b.

\underline{\sf{Given:}}

LCM = 72

Product (a,b) = 864.

∴ 72 × HCF = 864

\implies HCF = 864/72

\implies HCF = 12.

Answer : HCF = 12

Answered by Anonymous
28

\textbf{\underline{\underline{According\:to\:the\:Question}}}

★Some Full forms :-

☆HCF = Highest common Factor

☆LCM = Least common Factor

★Solution :-

★As per the definition we have :-

HCF × LCM = Product of two numbers

HCF × LCM = 864

★Here we have to substitute the value of LCM :-

{\boxed{\sf\:{HCF=\dfrac{864}{72}}}}

\fbox{HCF = 12}

\huge{\boxed{\sf\:{Additional\; Information}}}

In case :-

★Three positive integers a,b,c

★HCF(a,b,c) × LCM(a,b,c) ≠ a × b × c

\tt{\rightarrow LCM(a,b,c)=\dfrac{a\times b\times c\times HCF (a,b,c)}{HCF(a,b)\times HCF(b,c)\times HCF(a,c)}}\tt{\rightarrow HCF(a,b,c) =\dfrac{a\times b\times c\times LCM (a,b,c)}{LCM(a,b)\times LCM(b,c)\times LCM(a,c)}}

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