Question

The HCF of two numbers is 145 and their LCM is 2175. If one of the numbers is 725, fi nd the other.​

Answer 1

$\bf \underline{Given} :$ ↴

$\sf \implies HCF \: of \: the \: numbers = 145$

$\sf \implies LCM \: of \: the \: numbers = 2175$

$\sf \implies One \: number = 725$

$\bf \underline{To \: find} :$ ↴

$\sf \implies Other \: number = \: ?$

$\bf\underline{ \underline{Solution} }$

$\sf Let \: the \: other \: number \: be \: M$

$\sf \underline{We \: know \: that},$

$\boxed{ \pink{\sf Product \: of \: two \: numbers = LCM \times HCF }}$

$\sf \implies 725 \times M = 145 \times 2175$

$\sf \implies 725 \times M = 315375$

$\sf \implies M = \dfrac{315375}{725}$

$\sf \implies M = 435$

$\underline{ \boxed{ \pink{\sf Therefore, other \: the\:number \:is\:435 }}}$

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$\bf \underline{Let's \: verify \: our \: answer},$

$\sf \implies 725 \times 435= 145 \times 2175$

$\sf \implies 315375 = 315375$

$\red{ \bf \: Hence \: verified \: ! }$

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$\bf \underline{More \:to \:know} \: !$

LCM stands for Lowest common factor. It is the least number and LCM is exactly divisible by two or more numbers.

HCF stands for Highest common factor. It is the greatest factor between given any numbers.