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Question 70
The Least Common Multiple and Highest common Factor of two numbers are 30 and 5 respectively. If their sum is 25, then what will be the difference of these two numbers?
Solution
Let the two numbers be a and b.
We know that Product of two numbers = Product of their LCM and HCF.
Then, ab = 30*5 = 150
a+b = 25
$$(a-b)^2 = (a+b)^2 - 4ab = 25^2 - 4\times150 = 625-600 = 25$$
=> a-b = 5
Therefore, The difference between the numbers = 5.
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