1987 AMC 8 Problem 9 — Solution | LIVE by Po-Shen Loh

LIVE

English

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

$\dfrac12 + \dfrac13 + \dfrac14 + \dfrac15 + \dfrac16 + \dfrac17,$

what is the least common denominator used?

$120$

$210$

$420$

$840$

$5040$

Answer: C

Concepts:least common multiple

Difficulty rating: 800

Solution:

The least common multiple must include $4 = 2^2,$ $3,$ $5,$ and $7$ (the factor $6 = 2 \times 3$ is already covered).

So it is $4 \times 3 \times 5 \times 7 = 420.$

Thus, the correct answer is C .

← Problem 8#8 Full Exam Problem 10#10 →

Problem 9 in Other Years

1985 AMC 8 · 1986 AMC 8 · 1988 AMC 8 · 1989 AMC 8 · 1990 AMC 8 · 1991 AMC 8 · 1992 AMC 8 · 1993 AMC 8 · 1994 AMC 8 · 1995 AMC 8 · 1996 AMC 8 · 1997 AMC 8 · 1998 AMC 8 · 1999 AMC 8 · 2000 AMC 8 · 2001 AMC 8 · 2002 AMC 8 · 2003 AMC 8 · 2004 AMC 8 · 2005 AMC 8 · 2006 AMC 8 · 2007 AMC 8 · 2008 AMC 8 · 2009 AMC 8 · 2010 AMC 8 · 2011 AMC 8 · 2012 AMC 8 · 2013 AMC 8 · 2014 AMC 8 · 2015 AMC 8 · 2016 AMC 8 · 2017 AMC 8 · 2018 AMC 8 · 2019 AMC 8 · 2020 AMC 8 · 2022 AMC 8 · 2023 AMC 8 · 2024 AMC 8 · 2025 AMC 8 · 2026 AMC 8