AMC10 2001 A

AMC10 2001 A · Q8

AMC10 2001 A · Q8. It mainly tests GCD & LCM.

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?

学校的数学实验室有四位助教：Wanda、Darren、Beatrice 和 Chi。他们的工作安排如下：Darren 每三个学校日工作一次，Wanda 每四个学校日工作一次，Beatrice 每六个学校日工作一次，Chi 每七个学校日工作一次。今天他们都在数学实验室工作。从今天起多少学校日后他们将再次一起在实验室辅导？

(A) 42 42

(B) 84 84

(D) 178 178

(E) 252 252

Answer

Correct choice: (B)

正确答案：（B）

Solution

The number of school days until they will next be together is the least common multiple of 3, 4, 6, and 7, which is 84.

他们下次一起工作的学校日数是最小公倍数 3、4、6 和 7 的最小公倍数，即 84。

Topics

NT.003 GCD & LCM