17 and 19 are odd, consecutive integers whose product is 323.
Algebraic explanation:
Let x be the first unknown. Then x+2 must be the second unknown.
x⋅(x+2)=323 Set up equation
x2+2x=323 Distribute
x2+2x−323=0 Set equal to zero
(x−17)(x−19)=0 Zero product property
x−17=0orx−19=0 Solve each equation
x=17orx=19