2016 AMC 8 Problem 20
Attempt Problem 20 of the 2016 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2016 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
20.
The least common multiple of and is and the least common multiple of and is What is the least possible value of the least common multiple of and
Answer: A
Small hint:
Since appears in both least common multiples, start with possible values of .
Big hint:
Try to make absorb the common factor from and .
Video solution:
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Written solution:
We know that has to divide both and so it must equal either or
If then and making their least common multiple If then we may take and The least common multiple in this scenario is
Thus, A is the correct answer.
Problem 20 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
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