2001 AMC 10 第 8 题

Question

旺达、达伦、比阿特丽斯和奇是学校数学实验室的辅导员。他们的排班如下：达伦每三个上课日工作一次，旺达每四个上课日工作一次，比阿特丽斯每六个上课日工作一次，奇每七个上课日工作一次。今天他们四人都在数学实验室工作。从今天起再过多少个上课日，他们下一次会同时在实验室辅导？

Wanda, Darren, Beatrice, and Chi are tutors in the school math lab. Their schedule is as follows: Darren works every third school day, Wanda works every fourth school day, Beatrice works every sixth school day, and Chi works every seventh school day. Today they are all working in the math lab. In how many school days from today will they next be together tutoring in the lab?

42

84

126

178

252

答案：B

知识点：最小公倍数质因数分解

难度评级：960

小提示：

求

3

、

4

、

6

和

7

的最小公倍数。

Find the least common multiple of

3,

4,

6,

and

7

大提示：

最小公倍数需要包含因子

2^2

、

3

和

7

。

The least common multiple needs the factors

2^2,

3,

and

7

解答：

他们再次同时工作需要经过

\text{lcm}(3,4,6,7)

个上课日。因为

4=2^2

，

6=2\cdot3

，所以最小公倍数为

2^2\cdot3\cdot7=84

。

所以正确答案是 B。

They meet again after

\text{lcm}(3,4,6,7)

days. Since

4=2^2

and

6=2\cdot3,

the least common multiple is

2^2\cdot3\cdot7=84.

Thus, the correct answer is B.

2001 AMC 10 第 8 题

答案：B

难度评级：960

小提示：

大提示：

解答：

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