Let the three natural numbers be a, b and c. We know that a + b + c = 25.
Let us substitute some values and see where this is headed
a = 1, b = 2 c = 22, Product = 44
a = 2, b = 3 c = 20, product = 120
a = 5, b = 6 c = 14, product = 420
The numbers should be as close to each other as possible. (Just trial and error and one can figure this out). This property is an extension of the AM-GM Inequality.
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