Since the product of the two positive integers is $$100$$, the possible pairs of integers are $$\left( 1,100 \right)$$, $$\left( 2,50 \right)$$, $$\left( 4,25 \right)$$, $$\left( 5,20 \right)$$, $$\left( 10,10 \right)$$, the smaller the difference, the smaller the sum, so the smallest sum is $$10+10=20$$. 
What is the smallest possible sum of two positive integers with a product of $$100$$? 
Options:
  - $$100$$ 
  - $$52$$ 
  - $$29$$ 
  - $$25$$ 
  - $$20$$ 