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Question 61
The Least Common Multiple and Highest Common Factor of two numbers are 60 and 3 respectively. If their difference is 3, then what will be the sum of these two numbers?
Solution
Let the two numbers be a and b.
We know that the product of two numbers = Product of their LCM and HCF
ab = 3*60 = 180
Given, a - b = 3
We know that $$(a-b)^2 = (a+b)^2 - 4ab$$
$$3^2 = (a+b)^2 - 4\times180$$
=> $$9 = (a+b)^2 - 720$$
$$(a+b)^2 = 729 => a+b = 27$$
Therefore, Sum of the two numbers = 27
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