Find the largest two consecutive integers whose sum is less than 46

1. Let the two consecutive integers be n and n+1 .
2. Their sum is n + (n+1) = 2n + 1 .
3. To find the largest such integers, solve 2n + 1 < 46 .
4. Subtract 1 from both sides: 2n < 45 .
5. Divide by 2: n < 22.5 .
6. Since n must be an integer, the largest possible value for n is 22.

Thus, the integers are 22 and 23.