To find the two numbers on a 30 board that yield the largest product when multiplied together, you should select the two numbers that are closest to half of 30. In this case, the numbers 15 and 15 (since 15 + 15 = 30) will give the largest product, which is 225. If only distinct pairs are allowed, then 14 and 16 would be the next best option, resulting in a product of 224.
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