# SOLUTION: If the average of three different positive integers is 5, then the least possible product of these numbers is: Please help

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 Click here to see ALL problems on Average Question 704261: If the average of three different positive integers is 5, then the least possible product of these numbers is: Please helpAnswer by AnlytcPhil(1321)   (Show Source): You can put this solution on YOUR website!```To have an average of 5, the sum of the three must be 15. Here is a fact about positive numbers we can use: If two positive numbers have a certain sum, their product is largest when they are closest together and smallest when they are farthest apart. However, here we have three integers with that sum, not just two. So that complicates matters a bit. But, we can consider only two numbers and use that fact above. Here's how: Suppose the three integers are a, b, and c, where a < b < c. We can consider just two numbers, (a+b) and c. We want to choose (a+b) and c as far apart as possible. To do that we choose (a+b) as small as possible, which is 3, when a=1 and b=2, and that choice will make c as much larger than 3 as possible. In order to have sum 15, c must be 12, and 12 is as far away from 3 as we can get. So the smallest possible product is 1*2*12 = 24. Edwin```