13. A box of hawthorns has more than one hundred grains. When counted in groups of 3, there is 1 extra; when counted in groups of 4, there are 2 extra; when counted in groups of 5, there are 3 extra; when counted in groups of 6, there are 4 extra. The box of hawthorns has at most ( ) grains.
【Answer】 178
【Analysis】Complementary congruence type. The sum of the total number +2 is a multiple of $3,4,5,6$. $[3,4,5,6]=60$, enumeration yields a maximum of 178 grains.【Lecture Notes Comparison】Long-term class Autumn Lecture 11 on Divisors and Multiples, Homework 2, Type Question.