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Question 56
The Least Common Multiple and Highest Common Factor of two numbers are 60 and 4 respectively. If their sum is 32, then what will be the difference of these two numbers?
Solution
Let the two numbers be a and b.
Product of two numbers = Product of their LCM and HCF
Hence, ab = 4*60 = 240
Given, a+b = 32
$$(a-b)^2 = (a+b)^2-4ab$$
$$= 32^2-4\times240 = 1024-960 = 64$$
$$(a-b) = 8$$
Hence, The difference between the two numbers = 8.
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