AMC 12A 2022 Problem 23

Let h_{n} and k_{n} be the unique relatively prime positive integers such that

\dfrac{1}{1}+\dfrac{1}{2}+\dfrac{1}{3}+\cdots+\dfrac{1}{n}=\dfrac{h_{n}}{k_{n}}

Let L_{n} denote the least common multiple of the numbers 1,2,3, \ldots, n. For how many integers with 1 \leq n \leq 22 is k_{n}<L_{n} ?

Answer Choices
A. 0
B. 3
C. 7
D. 8
E. 10