The HCF and LCM of two numbers are 36 and 756 | vedclass

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(B) Given that $HCF = 36$ and $LCM = 756$.We know that the product of two numbers is equal to the product of their $HCF$ and $LCM$.Let the two numbers

Vedclass · Accepted Answer

$108, 252$

Vedclass · Answer

(B) Given that $HCF = 36$ and $LCM = 756$.We know that the product of two numbers is equal to the product of their $HCF$ and $LCM$.Let the two numbers be $36a$ and $36b$,where $a$ and $b$ are coprime numbers.Then,$HCF 	imes LCM = 36a 	imes 36b = 36 	imes 756$.Dividing both sides by $36^2$,we get $a 	imes b = \frac{756}{36} = 21$.The possible pairs of coprime factors of $21$ are $(1, 21)$ and $(3, 7)$.Case $1$: If $(a, b) = (1, 21)$,the numbers are $(36 	imes 1, 36 	imes 21) = (36, 756)$.Case $2$: If $(a, b) = (3, 7)$,the numbers are $(36 	imes 3, 36 	imes 7) = (108, 252)$.Comparing with the given options,the pair $(108, 252)$ is present.

The $HCF$ and $LCM$ of two numbers are $36$ and $756$ respectively. Find the possible pair of numbers.

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