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You could go for the extreme and say that, since both numbers are positive integers, the product is greater than 1. Also, since both numbers are smaller than 1000, the product is less than 1000*1000 = 1000000.
You could narrow it down to between 3*500 and 3*600 that is, in the range (1500, 1800).
If your mental arithmetic is good, you could do 3*560 and 3*570 = (1680, 1710).
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