The product of two 2-digit numbers is 2160 an | vedclass

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Question

(C) Let the two numbers be $12x$ and $12y$,where $x$ and $y$ are coprime.Given that the product of the numbers is $2160$,we have:$12x 	imes 12y = 216

Vedclass · Accepted Answer

$(36, 60)$

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(C) Let the two numbers be $12x$ and $12y$,where $x$ and $y$ are coprime.Given that the product of the numbers is $2160$,we have:$12x 	imes 12y = 2160$$144xy = 2160$$xy = \frac{2160}{144} = 15$Since $x$ and $y$ are coprime and their product is $15$,the possible pairs for $(x, y)$ are $(1, 15)$ or $(3, 5)$.If $(x, y) = (1, 15)$,the numbers are $12(1) = 12$ and $12(15) = 180$. However,$180$ is not a $2$-digit number.If $(x, y) = (3, 5)$,the numbers are $12(3) = 36$ and $12(5) = 60$. Both are $2$-digit numbers.Thus,the numbers are $(36, 60)$.

The product of two $2$-digit numbers is $2160$ and their $H.C.F.$ is $12$. The numbers are:

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