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Question 59
The Least Common Multiple and Highest Common Factor of two numbers are 75 and 5 respectively. If their difference is 10, then what will be the sum of these two numbers?
Solution
Let the two numbers be a and b.
Product of two numbers = Product of their LCM and HCF
ab = 5*75 = 375
a-b = 10
$$(a+b)^2 = (a-b)^2+4ab$$
=> $$(a+b)^2 = 10^2+4\times375$$ = 100+1500 = 1600$$
=> $$a+b = 40$$
Therefore, Sum of the two numbers = 40.
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