1987 AMC 8 Problem 9

Attempt Problem 9 of the 1987 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 1987 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

9.

When finding the sum
12+13+14+15+16+17,\dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 + \dfrac16 + \dfrac17,
what is the least common denominator used?
120120
210210
420420
840840
50405040
Answer: C
Concepts:least common multiple
Small hint:
The least common denominator is the least common multiple of 2,2, 3,3, 4,4, 5,5, 6,6, 77
Big hint:
Use 44 to cover the factor 44 (and 22), then include 3,3, 5,5, and 77
Solution:
The least common multiple must include 4=22,4 = 2^2, 3,3, 5,5, and 77 (the factor 6=2×36 = 2 \times 3 is already covered).
So it is 4×3×5×7=420.4 \times 3 \times 5 \times 7 = 420.
Thus, the correct answer is C .
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