The L.C.M. of two numbers is 120 and their H. | vedclass

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(D) Let the two numbers be $10x$ and $10y$,where $x$ and $y$ are coprime to each other.Given that the $H.C.F.$ is $10$,the numbers must be multiples o

Vedclass · Accepted Answer

$70$

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(D) Let the two numbers be $10x$ and $10y$,where $x$ and $y$ are coprime to each other.Given that the $H.C.F.$ is $10$,the numbers must be multiples of $10$.The $L.C.M.$ of $10x$ and $10y$ is $10xy$.We are given $10xy = 120$,which implies $xy = 12$.The possible pairs of $(x, y)$ such that they are coprime are $(1, 12)$ and $(3, 4)$.Case $1$: If the pair is $(1, 12)$,the numbers are $10(1) = 10$ and $10(12) = 120$. Their sum is $10 + 120 = 130$.Case $2$: If the pair is $(3, 4)$,the numbers are $10(3) = 30$ and $10(4) = 40$. Their sum is $30 + 40 = 70$.Comparing with the given options,$70$ is present.

The $L.C.M.$ of two numbers is $120$ and their $H.C.F.$ is $10.$ Which of the following can be the sum of those two numbers?

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