2003 AMC 8 Problem 19
Attempt Problem 19 of the 2003 AMC 8 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2003 AMC 8 solutions, or check the answer key.
All problems are used with official legal permission of the Mathematical Association of America (MAA).
19.
How many integers between and have all three of the numbers and as factors?
Answer: C
Small hint:
Use the least common multiple of and
Big hint:
Count the multiples of that LCM between and
Solution:
If a number has these three numbers as factors, then their least common multiple must also divide
These numbers have the following prime factorizations:
From these values, we get that the least common multiple is
Therefore, the multiples of between and are and
Thus, C is the correct answer.
Problem 19 in other years
- 1985 AMC 8
- 1986 AMC 8
- 1987 AMC 8
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- 1989 AMC 8
- 1990 AMC 8
- 1991 AMC 8
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