What is the smallest possible sum of two positive integers whose product is $$240$$？ 
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Since the product of the two positive integers is $$240$$, the possible pairs of integers are $$\left( 1,240 \right)$$, $$\left( 2,120 \right)$$, $$\left( 3,80 \right)$$, $$\left( 4,60 \right)$$, $$\left( 5,48 \right)$$, $$\left( 6,40 \right)$$, $$\left( 8,30 \right)$$, $$\left( 10,24 \right)$$, $$\left( 12,20 \right)$$ and $$\left( 15,16 \right)$$. The respective sums of these pairs are $$241$$, $$122$$, $$83$$, $$64$$, $$53$$, $$46$$, $$38$$, $$34$$, $$32$$ and $$31$$. Of these, the smallest value is $$31$$. 