eybrj2 wrote:
If n is the least of 3 consecutive positive integers and n is odd, what is the least common multiple of the 3 integers, in terms of n?
A. n(n+1)(n+2)
B. n^3 + 3
C. n(n^2 + 2)
D. n^2 + 3
E. 3(n +1)
Two consecutive integers are co-prime, meaning that they do not share any common factor but 1. For example 4 and 5 are consecutive integers and they do not share any common factor but 1. This means that the leas common multiple of two consecutive integers is always their product: LCM(4, 5)=20.
So, for n, n+1 and n+2 each pair consecutive terms is co-prime (n and n+1, as well as n+1 and n+2). Now, since n is odd, then n and n+2 are also co-prime (consecutive odd integers are also co-prime: 3 and 5, 5 and 7, 7 and 9, ...), which means that all 3 integers are co-prime to each other, hence the least common multiple of the 3 integers is n(n+1)(n+2).
Answer: A.
Else you can pick some number for n, say 3. Then three consecutive integers will be 3, 4, and 5, their LCM is 3*4*5=60. Now, just plug 3 in the answer choices to see which yields 60: only A.
Note that for plug-in method it might happen that for some particular number(s) more than one option may give "correct" answer. In this case just pick some other numbers and check again these "correct" options only. For example if you pick n=1 then you get two "correct" choices A and E.
Hope it helps.
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
close
88% (01:17) correct 
