For two consecutive positive integers a and b | vedclass

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Question

(A) For any two positive integers $a$ and $b$,the relationship between their Highest Common Factor $(HCF)$ and Least Common Multiple $(LCM)$ is given

Vedclass · Accepted Answer

$a 	imes b$

Vedclass · Answer

(A) For any two positive integers $a$ and $b$,the relationship between their Highest Common Factor $(HCF)$ and Least Common Multiple $(LCM)$ is given by the formula: $	ext{HCF}(a, b) 	imes 	ext{LCM}(a, b) = a 	imes b$.Since $a$ and $b$ are consecutive positive integers,they are coprime,meaning their only common factor is $1$. Thus,$	ext{HCF}(a, b) = 1$.Substituting this into the formula,we get $1 	imes 	ext{LCM}(a, b) = a 	imes b$,which simplifies to $	ext{LCM}(a, b) = a 	imes b$.Therefore,$	ext{HCF}(a, b) 	imes 	ext{LCM}(a, b) = 1 	imes (a 	imes b) = a 	imes b$.

For two consecutive positive integers $a$ and $b$,what is the value of $\text{HCF}(a, b) \times \text{LCM}(a, b)$?

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