AMC 8 1987 Problem 9

AMC8 1987 年第 9 题

整除与因数★★☆☆☆

When finding the sum

\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}

, the least common denominator used is

求

\displaystyle \frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\frac{1}{5}+\frac{1}{6}+\frac{1}{7}

的和时，使用的最小公分母是

A.120
B.210
C.420
D.840
E.5040

正确答案 · Correct Answer

C

解析 · Solution

Solution 1

The least common denominator is

\mathrm{lcm}(2, 3, 4, 5, 6, 7) = \mathrm{lcm}(2, 3, 2^2, 5, 2\cdot 3, 7) = 2^2 \cdot 3 \cdot 5 \cdot 7 = 420

.

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