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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Updated on: 10-Oct-2022

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