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When u take an L

Source: AMC 10A Problem 19

November 11, 2022
AMCAMC 10AMC 10 A2022 AMC 10a2022 AMCleast common multiple

Problem Statement

Define LnL_n as the least common multiple of all the integers from 11 to nn inclusive. There is a unique integer hh such that 11+12+13…+117=hL17\frac{1}{1}+\frac{1}{2}+\frac{1}{3} \ldots +\frac{1}{17}=\frac{h}{L_{17}}. What is the remainder when hh is divided by 17?17?
<spanclass=′latex−bold′>(A)</span>1<spanclass=′latex−bold′>(B)</span>3<spanclass=′latex−bold′>(C)</span>5<spanclass=′latex−bold′>(D)</span>7<spanclass=′latex−bold′>(E)</span>9<span class='latex-bold'>(A) </span> 1 \qquad <span class='latex-bold'>(B) </span> 3 \qquad <span class='latex-bold'>(C) </span> 5 \qquad <span class='latex-bold'>(D) </span> 7 \qquad <span class='latex-bold'>(E) </span> 9
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