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Smallest Common Multiple

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by leumas » Wed Sep 14, 2011 8:55 am
barracuda939 wrote:Can you help me over here Stuart?

The question states that what is the smallest common multiple of two numbers greater than 250.

In this case,
the two numbers = 251 and 251.

Multples of 251 : 251,502.....
Thus smallest = 251.

But if the question were to ask DISTINCT numbers, how could the answer be 502?
251: 251,502
252: 252, 504...
Hi, let me play Stuart for sometime to clear you :)

The question asks for "Smallest" common multiple for two "Integers" greater than 250

The smallest digit is 251 and the next possible integer which is a multiple of 251 is 502, which gives us the "Smallest" common multiple of 502!!

Hope I played well ;-)
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by Deependra1 » Tue Nov 08, 2011 3:21 am
ANSWER: C
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by Sharma_Gaurav » Mon Jan 09, 2012 3:35 pm
answer A is correct.
two integers condition is not given ( whether equal or different) hence to find smallest answer, consider then same numbers -> is the trick
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by asax » Sat Jul 07, 2012 2:14 am
Stuart Kovinsky Great explanation.
Looking forward to 2013 MBA admissions!
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by Ganesh hatwar » Mon Jul 16, 2012 11:09 pm
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
A.. two numbers 251 and 251 >250
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by confuse mind » Wed Jul 18, 2012 7:07 pm
Did the same mistake of taking the number as distinct and chose 502 :(


Thanks Staurt
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by Ravipprasad » Thu Oct 11, 2012 6:01 am
Stuart Kovinsky wrote:
niksdoon wrote:Hi Stuart,

What if question would've included "distinct" in the question. What would have been our answer in that case?

I couldn't understand solution provided by akhp77.

Please advise !!

Thanks,
Niks
I made the mistake of assuming distinct and chose 502. But when it says 2, shouldn't we choose 2?

With "distinct" the answer would have been 502; to generate the smallest common multiple of two distinct numbers, both greater than 250, we take the smallest number we can (251) and then double it (502) - the SCM of 251 and 502 is 502.
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by rajeshsinghgmat » Fri Feb 01, 2013 1:06 am
A for Answer.

251*1,251*2
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by tamiri » Fri Jun 28, 2013 11:21 pm
Hi,
In the case of distinct nubers, say 251 and 252, isn't the LCM is their multiple hence 251*252=63252?
Many posted that it would be 252. What am I missing?
Tamir
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by glensuchitha » Wed Aug 21, 2013 9:21 pm
Hey guys,

This is how I rationalized the question.

The LCM is nothing but multiples of the lowest prime number(s),
Therefore, 251 is the only prime number in the choices given, hence, it is A.
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by ndqv » Fri Aug 30, 2013 11:53 pm
Assumption: 2 integers are different
2 integers >= 251
The 1st number is 251, the 2nd the smallest multiple of 251 or 502
If so, the common multiple is 502

Another way is to look at answer choices: 251 and 252 is too small; for 502 we have 2 numbers 251 and 502

In short, choose C
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by rajeshsinghgmat » Wed Sep 04, 2013 6:08 am
251*1

251*2
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by elexdeepak » Sat Nov 16, 2013 6:09 am
I was totally stumped seeing the question as i could not understand the requirement, More or less have understood the question but would still ask stuart to give some more clarity.

Thanks
Deepak
Stuart Kovinsky wrote:
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
Hi,

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).
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by Mathsbuddy » Mon Dec 02, 2013 12:09 am
(A) 251

(Both integers can be the same)
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by Mathsbuddy » Mon Dec 02, 2013 12:13 am
leumas wrote:
barracuda939 wrote:Can you help me over here Stuart?

The question states that what is the smallest common multiple of two numbers greater than 250.

In this case,
the two numbers = 251 and 251.

Multples of 251 : 251,502.....
Thus smallest = 251.

But if the question were to ask DISTINCT numbers, how could the answer be 502?
251: 251,502
252: 252, 504...
Hi, let me play Stuart for sometime to clear you :)

The question asks for "Smallest" common multiple for two "Integers" greater than 250

The smallest digit is 251 and the next possible integer which is a multiple of 251 is 502, which gives us the "Smallest" common multiple of 502!!

Hope I played well ;-)
Good effort, but...
1) The question doesn't say that the integers have to be different;
2) 251 is not a digit, it is an integer (a whole number). While digits are integers too, they are simply the ten single numbers: 0,1,2,3,4,5,6,7,8 and 9.
Just a detail, which might be useful in future problem solving.
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