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2022 AMC 10A Problem 19

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2022 AMC 10A Problem 19AMC 10 Step by Step

Name: Date: September 13, 2026

Modular Arithmetic · difficulty 4 of 5 · about 6 min · position P16-20

Define $L_n$ as the least common multiple of all the integers from $1$ to $n$ inclusive. There is a unique integer $h$ such that $\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+\cdots+\frac{1}{17}=\frac{h}{L_{17}}$ What is the remainder when $h$ is divided by $17$ ?

A)
$1$
B)
$3$
C)
$5$
D)
$7$
E)
$9$

2022 AMC 10A Problem 19

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