Last visit was: 12 Jul 2024, 19:34 It is currently 12 Jul 2024, 19:34
Toolkit
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

# If n is the least of 3 consecutive positive integers and

SORT BY:
Tags:
Show Tags
Hide Tags
Manager
Joined: 31 Oct 2011
Posts: 200
Own Kudos [?]: 7963 [21]
Given Kudos: 18
Math Expert
Joined: 02 Sep 2009
Posts: 94302
Own Kudos [?]: 640182 [19]
Given Kudos: 84576
General Discussion
Alum
Joined: 12 Aug 2015
Posts: 2272
Own Kudos [?]: 3195 [1]
Given Kudos: 893
GRE 1: Q169 V154
Intern
Joined: 13 Sep 2018
Posts: 2
Own Kudos [?]: 0 [0]
Given Kudos: 0
Re: If n is the least of 3 consecutive positive integers and [#permalink]
It seems like A is the answer whether N is even or odd. Are they just throwing in that N is odd to throw us off?
Manager
Joined: 24 Dec 2017
Posts: 139
Own Kudos [?]: 67 [2]
Given Kudos: 48
Location: India
Concentration: Strategy, Real Estate
Schools: Johnson '21
Re: If n is the least of 3 consecutive positive integers and [#permalink]
2
Bookmarks
n = odd & least of 3 consecutive positive integers(n,n+1,n+2)

I took n as 3 and the other 2 numbers are 4 & 5

LCM of 3,4,5 = 60

Plug in 3 on each options and the answer should equal to LCM.

A. n(n+1)(n+2)
=>3.4.5
=>60

GMAT Club Legend
Joined: 18 Aug 2017
Posts: 7962
Own Kudos [?]: 4207 [0]
Given Kudos: 243
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Re: If n is the least of 3 consecutive positive integers and [#permalink]
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)

let no be 1,2,3
LCM ; 1*2*3 ; 6
n=1
option A ; is valid
Board of Directors
Joined: 11 Jun 2011
Status:QA & VA Forum Moderator
Posts: 6049
Own Kudos [?]: 4763 [0]
Given Kudos: 463
Location: India
GPA: 3.5
Re: If n is the least of 3 consecutive positive integers and [#permalink]
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)

Plug in any value and check , let the 3 nos be 1 , 2 & 3

LCM of ( 1,2,3) = 6

Check the options -

(A) 1*2*3 = 6 (Possible)
(B) 1^3 + 3 = 4 (Not possible)
(C) 1(1^2 + 2) = 3 (Not possible)
(D) 1^2 + 3 = 4 (Not possible)
(E) 3 ( 1 + 1 ) = 6 (POssible)

Now check with
Archit3110 wrote:
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)

let no be 1,2,3
LCM ; 1*2*3 ; 6
n=1
option A ; is valid

Here is why we need tp check all the options carefully as (E) will yeild the same result in this case of 1 ,2 & 3 and hence we need to plug in once again to confirm with 3,4 & 5 as ArjunJag1328
has done...

Correct Answer will definitely be (A)
VP
Joined: 14 Feb 2017
Posts: 1086
Own Kudos [?]: 2186 [1]
Given Kudos: 368
Location: Australia
Concentration: Technology, Strategy
GMAT 1: 560 Q41 V26
GMAT 2: 550 Q43 V23
GMAT 3: 650 Q47 V33
GMAT 4: 650 Q44 V36
GMAT 5: 600 Q38 V35
GMAT 6: 710 Q47 V41
WE:Management Consulting (Consulting)
Re: If n is the least of 3 consecutive positive integers and [#permalink]
1
Kudos
Testing x=1 will eliminate answers B,C,D but A and E will both produce the same result, so test x=3 to determine that A is correct.
GMAT Club Legend
Joined: 03 Oct 2013
Affiliations: CrackVerbal
Posts: 4918
Own Kudos [?]: 7796 [0]
Given Kudos: 220
Location: India
Re: If n is the least of 3 consecutive positive integers and [#permalink]
Top Contributor
Since the smallest of the 3 consecutive positive integers is odd, the 3 consecutive integers will be co-prime to each other.
Therefore, LCM of the 3 consecutive positive integers = n (n+1) (n+2).

We can take a few examples to be sure.
If n =1, n+1 = 2 and n+2 = 3. LCM = 6
If n = 3, n+1 = 4 and n+2 = 5. LCM = 60.

The correct answer option is A.

This can now become a property that you can add to the repository of Number properties.

Hope that helps!
Aravind BT
Intern
Joined: 12 May 2024
Posts: 43
Own Kudos [?]: 21 [0]
Given Kudos: 43
Re: If n is the least of 3 consecutive positive integers and [#permalink]
­Given three consecutive positive integers where n is the smallest and is odd, we need to determine the least common multiple (LCM) of these three integers in terms of n.

Let the three consecutive integers be n, n+1, and n+2.

First, let's consider the prime factorizations of these three integers:

1. n: Since n is odd, it does not include the prime factor 2.
2. n+1: Since n is odd, n+1 is even. Therefore, n+1 includes the prime factor 2.
3. n+2: Since n is odd, n+2 is odd and does not include the prime factor 2.
For the least common multiple, we need the highest power of all prime factors that appear in the factorizations of n, n+1, and n+2

LCM:

• The prime factor 2 will appear because n+1 is even.
• Any odd prime factors will come from n, n+1, and n+2.
Let's look at the product of n, n+1, and n+2:

n(n+1)(n+2)Since n, n+1, and n+2 are three consecutive numbers, their product includes all necessary factors, but we are interested in the LCM, not just the product.

Simplification:

We should check if there is any redundancy in the factors:

1. If n or n+2 is a multiple of 3, the highest power of 3 will be included.
2. If n is odd, then one of n or n+2 might have additional factors which could reduce to lower powers.
3. The number n+1 will include the factor 2 and other odd primes.
Because n is odd and n is not a multiple of 2, n+1 is the only even number contributing the highest power of 2.

Conclusion:

The LCM of n, n+1, and n+2 is the product of the highest powers of all prime factors in these three numbers. Given the properties of consecutive numbers, there are no common factors beyond those explicitly present in each number.

Thus, the LCM is:

n(n+1)(n+2)This ensures we include all unique prime factors at their highest powers.
Re: If n is the least of 3 consecutive positive integers and [#permalink]
Moderator:
Math Expert
94302 posts