AMC 8 2016 Problem 20

AMC8 2016 年第 20 题

整除与因数★★★☆☆

The least common multiple of

a

and

b

is 12 , and the least common multiple of

b

and

c

is 15 . What is the least possible value of the least common multiple of

a

and

c

a 和 b 的最小公倍数是 12，b 和 c 的最小公倍数是 15，问 a 和 c 的最小公倍数的最小可能值是多少？

正确答案 · Correct Answer

解析 · Solution

Solution 1

We wish to find possible values of

a

b

, and

c

. By finding the greatest common factor of 12 and 15, we can find that

b

is 3. Moving on to

a

and

c

, in order to minimize them, we wish to find the least such that the least common multiple of

a

and 3 is 12,

\rightarrow 4

. Similarly, with 3 and

c

, we obtain 5. The least common multiple of 4 and 5 is

20 \rightarrow 20

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