Question 127

The LCM of two numbers is 168 and their HCF is 12. If the difference between the numbers is 60. what is the sum of the numbers?

Solution

Let the two numbers be a and b.
Product of two numbers = Product of their LCM and HCF
ab = 168*12 = 2016
Given, a-b = 60
$$(a+b)^2 = (a-b)^2+4ab$$
$$(a+b)^2 = 60^2+4\times2016 = 3600+8064 = 11664$$
Then, $$a+b = 108$$
Therefore, Sum of two numbers = 108.

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