2013 AMC 8 Problem 10
Attempt Problem 10 of the 2013 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 2013 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
10.
What is the ratio of the least common multiple of and to the greatest common factor of and
Answer: C
Small hint:
Prime-factorize both numbers.
Big hint:
The LCM uses the larger prime powers, while the GCF uses the smaller ones.
Video solution:
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Written solution:
Prime-factorize the two numbers:
The greatest common factor uses the smaller powers, so it is . The least common multiple uses the larger powers, so it is Therefore the desired ratio is .
Thus, C is the correct answer.
Problem 10 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
- 1988 AMC 8
- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
- 1992 AMC 8
- 1993 AMC 8
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