Two numbers,both greater than 29,have HCF 29 | vedclass

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Question

(C) Let the two numbers be $29x$ and $29y$,where $x$ and $y$ are coprime.Given that $LCM = 29 	imes x 	imes y = 4147$.Therefore,$xy = \frac{4147}{29

Vedclass · Accepted Answer

$696$

Vedclass · Answer

(C) Let the two numbers be $29x$ and $29y$,where $x$ and $y$ are coprime.Given that $LCM = 29 	imes x 	imes y = 4147$.Therefore,$xy = \frac{4147}{29} = 143$.The factors of $143$ are $(1, 143)$ and $(11, 13)$.If we choose $(1, 143)$,the numbers are $29 	imes 1 = 29$ and $29 	imes 143 = 4147$. However,the problem states that both numbers must be greater than $29$.If we choose $(11, 13)$,the numbers are $29 	imes 11 = 319$ and $29 	imes 13 = 377$.Both $319$ and $377$ are greater than $29$.Therefore,the sum of the numbers is $319 + 377 = 696$.

Two numbers,both greater than $29$,have $HCF$ $29$ and $LCM$ $4147$. The sum of the numbers is

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