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The HCF and LCM of two numbers are 9 and 819 respectively. One of the numbers is a two-digit number. Find the numbers.
Given:
One of the numbers is a two-digit number. Find the numbers.
One of the numbers is a two-digit number
To do: To find the other number
Solution:
Lets take the two numbers $x \ and \ y$
H C F of $x , y = 9$
So, $x \ and \ y$ has 9 as the common factor,
L C M of $x , y = 819 = 7 \times 9 \times 13$
Product of two numbers = L C M $\times$ H C F
$x \times y = 7 \times 9 \times 13 \times 9$
We can frame more numbers from the above, but one of the number should be in two digit,
$x \times y = 819 \times 9$ (cannot be this one)
$x \times y = 91 \times 9 or x \times y = 9 \times 91$
So, the numbers are $9 , 91$
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