Difference between revisions of "2022 AMC 10A Problems/Problem 19"
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Define <math>L_n</math> as the least common multiple of all the integers from <math>1</math> to <math>n</math> inclusive. There is a unique integer <math>h</math> such that | Define <math>L_n</math> as the least common multiple of all the integers from <math>1</math> to <math>n</math> inclusive. There is a unique integer <math>h</math> such that | ||
| − | + | <math>\frac{1}{1}+\frac{1}{2}+\frac{1}{3}\ldots+\frac{1}{17}=\frac{h}{L_{17}}</math> | |
What is the remainder when <math>h</math> is divided by <math>17</math>? | What is the remainder when <math>h</math> is divided by <math>17</math>? | ||
<math>\textbf{(A) } 1 \qquad \textbf{(B) } 3 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 7 \qquad \textbf{(E) } 9</math> | <math>\textbf{(A) } 1 \qquad \textbf{(B) } 3 \qquad \textbf{(C) } 5 \qquad \textbf{(D) } 7 \qquad \textbf{(E) } 9</math> | ||
Revision as of 02:27, 12 November 2022
Problem
Define 
as the least common multiple of all the integers from 
to 
inclusive. There is a unique integer 
such that
What is the remainder when is divided by 
?
