Hello Sir, Why is 251 the smallest multiple? It should be zero. Please guide.Stuart Kovinsky wrote:Hi,deepesh.gupta wrote:What is the smallest common multiple of two integers which are both greater than 250?
1) 251
2) 252
3) 502
4) 750
5) 884
we have to be very careful about not making assumptions on the GMAT; the GMAT uses very precise language and we should never "read in" a word that isn't actually there.
One commonly tested case involves the word "distinct", which simply means "different" - you have to be very careful not to add that word to a question.
This question is a perfect example - nowhere does it say that the two integers have to be distinct integers.
Accordingly, we can pick 251 and 251 as our two integers, which have a lowest common multiple of 251: choose (1).
BREAKING: Target Test Prep releases Brand New 2026 On Demand GMAT prep course
Redeem
Featured Course
Target Test Prep GMAT OnDemand
Scott Woodbury-Stewart’s private virtual classroom — 400 hours of master-class video lessons for the GMAT Focus Edition.
- 715+ score guarantee — highest in the industry (99th percentile)
- 52 chapters · 1,500+ lessons · 4,000+ practice questions
- 400 hours of video · 1,500+ instructor-led HD smartboard lessons
- 300,000+ students accepted to Harvard, Stanford, Wharton, Booth & Sloan & more
- 24/7 live support + weekly Zoom office hours with GMAT instructors
- TTP AI Assist — 24/7 AI-powered virtual tutor for instant help
- 1,200+ flashcards + AI-powered study assistant & daily calendar
- OnDemand, LiveTeach & GMAT Bootcamp formats available
- Also: GRE, SAT Math & Executive Assessment courses
- MBA Admissions Consulting now available
- 🏆 2025 EdTech Breakthrough Award: Test Prep Solution Provider of the Year
- 200,000+ students served
- 5-day free trial — $0 to start, no auto-billing, cancel anytime
★★★★★
5.0
(559 reviews)
130-pt guarantee
$0 to start
then $127/mo
Smallest Common Multiple
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
Good point, Zeeusuf.Zeeusuf wrote:
Hello Sir, Why is 251 the smallest multiple? It should be zero. Please guide.
In fact, -251 is also a common multiple of 251 and 251.
For the answer to be 251, this question requires some wording that restricts the multiples to POSITIVE integers only.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
Yes, I agree that the answer is incorrect. More importantly, the question is poorly worded.Zeeusuf wrote:Hello Brent,
Thanks!
So you agree that the answer is incorrect? It should be zero.
Regards,
Zee
I don't, however, think the correct answer is zero.What is the smallest common multiple of two integers which are both greater than 250?
1) 251
2) 252
3) 502
4) 750
5) 884
As it stands, the question does not have an answer.
For example, if the two integers are 251 and 251, then they have INFINITELY MANY common multiples, including ...753, 502, 251, 0, -251, -502, -753, ....
As you can see, there is no LEAST common multiple.
So, for there to be a correct answer we need to restrict the multiples to POSITIVE integers only.
We might word the question as follows:
If POSITIVE INTEGER k is a common multiple of two integers which are both greater than 250, what is the least value of k?
A) 251
B) 252
C) 502
D) 750
E) 884
Answer: A
Cheers,
Brent
Last edited by Brent@GMATPrepNow on Mon Jun 15, 2015 6:22 am, edited 1 time in total.
Brent Hanneson - Creator of GMATPrepNow.com
This is an apropos discussion, as there's even an official GMAT question, available in the new Exam Pack, that seems to me to make this same mistake. I asked the GMAC rep on BTG for some insight into their thinking, but she hasn't responded yet. (The thread is here. The official answer is E, but the actual answer is A.)
My take on all this: the Least Common Multiple (LCM) is explicitly defined as the least POSITIVE common multiple of x and y. Without that definition (or some equivalent), there is no smallest common multiple, since we can pick an arbitrarily small negative common multiple. (For instance, -6 is a multiple of 3 and 2, but so is -12, and -24, etc.) So a term like "smallest common multiple" is self-contradicting, unless it's the smallest common multiple of 0 and 0, which wouldn't be terribly interesting!
My take on all this: the Least Common Multiple (LCM) is explicitly defined as the least POSITIVE common multiple of x and y. Without that definition (or some equivalent), there is no smallest common multiple, since we can pick an arbitrarily small negative common multiple. (For instance, -6 is a multiple of 3 and 2, but so is -12, and -24, etc.) So a term like "smallest common multiple" is self-contradicting, unless it's the smallest common multiple of 0 and 0, which wouldn't be terribly interesting!
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
Not true.nikhilgmat31 wrote:0 is not multiple of an integer.
From the Official Guide:
If x and y are integers, then x is a divisor (factor) of y provided that and y = xn for some integer n. In this case, y is also said to be divisible by x or to be a multiple of x.
So, for example, since we can write 0 = (0)(3), we can say that 0 is a multiple of 3. We can also say that 0 is divisible by 3.
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Location: Vancouver, BC
- Thanked: 5254 times
- GMAT Score:770
Well, to get really picky, -20 is also a multiple of 4 and 5 (and -20 is LESS THAN 0)nikhilgmat31 wrote:HI Brent
If 0 is multiple of any integer then
LCM of 4 & 5 should be 0 not 20.
Please suggest.
-40 is also a multiple of 4 and 5
So is -2,000,000
There is no least common multiple of 4 and 5.
This is precisely why the GMAT typically restricts the numbers to POSITIVE VALUES when it comes to questions involving integer properties.
For example, check out these official questions:
- https://www.beatthegmat.com/lowest-posit ... 11361.html
- https://www.beatthegmat.com/og-13-ps-95- ... 81925.html
- https://www.beatthegmat.com/positive-neg ... t9905.html
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
I addressed this about a few posts earlier, check the (long) explanation there.nikhilgmat31 wrote:HI Brent
If 0 is multiple of any integer then
LCM of 4 & 5 should be 0 not 20.
Please suggest.
The short answer is that LCM is defined as the least common POSITIVE multiple.
Otherwise there would not be an LCM, since you could take arbitrarily small negative common multiples.
-
GMATinsight
- Legendary Member
- Posts: 1100
- Location: New Delhi, India
- Thanked: 205 times
P.S. Have made a small modification in question to make it a little betterdeepesh.gupta wrote:What is the smallest common multiple of two DISTINCT integers which are both greater than 250?
1) 251
2) 252
3) 502
4) 750
5) 884
First Number greater than 250 = 251
Second Number with maximum factor of it common with first number = 502 (smallest integer multiple of 251 greater than 251)
LCM = 502
Answer: Option C
"GMATinsight"Bhoopendra Singh & Sushma Jha
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
Most Comprehensive and Affordable Video Course 2000+ CONCEPT Videos and Video Solutions
Whatsapp/Mobile: +91-9999687183 l [email protected]
Contact for One-on-One FREE ONLINE DEMO Class Call/e-mail
Most Efficient and affordable One-On-One Private tutoring fee - US$40-50 per hour
