Question
The LCM and HCF of two numbers is 192 and 16 respectively.
If the sum of the number is 112, then find the difference between the numbers.Solution
We know that, LCM X HCF = product of the numbers
Let the numbers are 'a' and 'b'.
So, a X b = 192 X 16
So, ab = 3072........(I)
Given, a + b = 112
From equation (I) ,
Or, 'a' = (3072/b)
So, (3072/b) + b = 112
So, 3072 + b 2 = 112b
Or, b 2 - 112b + 3072 = 0
Or, b 2 - 64b - 48b + 3072 = 0
So, 'b' = 48 or 64
When, 'b' = 48
So, 'a' = (3072/48) = 64
When, 'b' = 64
So, 'a' = (3072/64) = 48
Therefore, required difference = 64 - 48 = 16
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