What is the largest multiple of 37 which is less than 800?
Dividing 800 by 37 gives a quotient of 21 with a remainder of 23. In other words,  \[
800 = 37 \cdot 21 + 23.
\]Thus $37\cdot 21 = \boxed{777}$ is the largest multiple of 37 which is less than 800.