The product of four consecutive integers is divisible by 13 and 31? what are the four consecutive integers if the product is as small as possible?

$L C M = 13 \cdot 31 = 403$
If we want the product to be as small as possible, we would have the other three integers be $400 , 401 , 402$.
Therefore, the four consecutive integers are $400 , 401 , 402 , 403$.