The H.C.F. and L.C.M. of two numbers are 12 a | vedclass

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(C) Let the two numbers be $12x$ and $12y$,where $x$ and $y$ are coprime (i.e.,their $H.C.F.$ is $1$).The $L.C.M.$ of these two numbers is given by $1

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$2$

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(C) Let the two numbers be $12x$ and $12y$,where $x$ and $y$ are coprime (i.e.,their $H.C.F.$ is $1$).The $L.C.M.$ of these two numbers is given by $12xy$.According to the problem,$12xy = 924$.Dividing both sides by $12$,we get $xy = \frac{924}{12} = 77$.Now,we need to find pairs of coprime factors $(x, y)$ such that their product is $77$.The factors of $77$ are $1, 7, 11, 77$.The possible pairs $(x, y)$ are $(1, 77)$ and $(7, 11)$.Since both pairs consist of coprime numbers,there are $2$ such pairs.

The $H.C.F.$ and $L.C.M.$ of two numbers are $12$ and $924,$ respectively. Then the number of such pairs is

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