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Intern  Joined: 11 Sep 2011
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What is the smallest possible common multiple of two integer  [#permalink]

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20 00:00

Difficulty:   65% (hard)

Question Stats: 45% (01:01) correct 55% (01:15) wrong based on 714 sessions

### HideShow timer Statistics What is the smallest possible common multiple of two integers which are both greater than 250?

A. 251
B. 252
C. 502
D. 750
E. 884
Math Expert V
Joined: 02 Sep 2009
Posts: 56276
Re: What is the smallest possible common multiple of two integer  [#permalink]

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summer101 wrote:
Bunuel wrote:
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

What if the 2 integers were said to be distinct? How do you solve than?

In this case the answer would be 502. Take the lowest integer more than 250, so 251 and multiply by 2. The LCM of 251 and 502 is 502.

Hope it's clear.
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Math Expert V
Joined: 02 Sep 2009
Posts: 56276
Re: What is the smallest possible common multiple of two integer  [#permalink]

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4
3
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

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What is the smallest common multiple of two integers which  [#permalink]

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To have the smallest possible is to have 251 and 251. Their common multiple is 251. Answer: A
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Re: What is the smallest possible common multiple of two integer  [#permalink]

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Bunuel wrote:
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

What if the 2 integers were said to be distinct? How do you solve than?
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Intern  Joined: 15 Nov 2011
Posts: 2
Re: What is the smallest possible common multiple of two integer  [#permalink]

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I'm confused by the wording of the question and even more confused by the question when you add in the hypothetical "distinct."

"Smallest multiple of two numbers" leads me to think that they're asking for the LCM. So the LCM of 251 and 251 is 251. Ok so now I feel that I understand this part.

"Smallest multiple of two distinct numbers" not sure about this one. So 251 and 252 would be my hypothetical terms. Not quite sure how you get 502 without doing long division and then factoring, which is time consuming.

How does 251 * 2 solve the distinct criteriea for the hypothetical addition to the original question?

Any help would be greatly appreciated.

Thanks!
Math Expert V
Joined: 02 Sep 2009
Posts: 56276
Re: What is the smallest possible common multiple of two integer  [#permalink]

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jbca wrote:
"Smallest multiple of two distinct numbers" not sure about this one. So 251 and 252 would be my hypothetical terms. Not quite sure how you get 502 without doing long division and then factoring.

Any help would be greatly appreciated.

Thanks!

The smallest integer greater then 250 is 251. The lowest multiple of 251, which is more than 251 is 502.
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Intern  Joined: 14 Jan 2013
Posts: 3
Location: Austria
Re: What is the smallest possible common multiple of two integer  [#permalink]

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Bunuel, can you please suggest some other/similar questions that are testing this topic? Thank you.
Math Expert V
Joined: 02 Sep 2009
Posts: 56276
Re: What is the smallest possible common multiple of two integer  [#permalink]

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Retired Moderator S
Joined: 18 Sep 2014
Posts: 1100
Location: India
Re: What is the smallest possible common multiple of two integer  [#permalink]

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Made a mistake by assuming that the two numbers indicate two distinct integers.
Need to be much more cautious with the wording of the question.
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Re: What is the smallest possible common multiple of two integer  [#permalink]

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1
I find this question a bit problematic.
It does not specifically include the words "from the following" or "among the following".
To demonstrate, zero is a multiple of every number, and 0 < 251. And I think it is possible to find smaller multiples if we consider multiples that are negative integers. Any thoughts?
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Re: What is the smallest possible common multiple of two integer  [#permalink]

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Bunuel wrote:
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

But we ain't even told that the numbers are same!  Math Expert V
Joined: 02 Sep 2009
Posts: 56276
Re: What is the smallest possible common multiple of two integer  [#permalink]

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rever08 wrote:
Bunuel wrote:
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

But we ain't even told that the numbers are same!  The point is that they could be the same and in this case we get the smallest possible common multiple.
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Location: India
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WE: Business Development (Energy and Utilities)
Re: What is the smallest possible common multiple of two integer  [#permalink]

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Hi
As the question ask for two numbers "which are Both" greater than 250.
Shouldn't it be distinct numbers?

Bunuel wrote:
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

Posted from my mobile device
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Math Expert V
Joined: 02 Sep 2009
Posts: 56276
Re: What is the smallest possible common multiple of two integer  [#permalink]

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gmatbusters wrote:
Hi
As the question ask for two numbers "which are Both" greater than 250.
Shouldn't it be distinct numbers?

Bunuel wrote:
babusona wrote:
What is the smallest possible common multiple of two integers which are both greater then 250?
1. 251
2. 252
3. 502
4. 750
5. 884

Notice that we are not told that the two integers must be distinct. So, if they both equal to 251 then the LCM of 251 and 251 is 251 itself.

Posted from my mobile device

Both must be greater than 250 but there is no indication that they must be different.
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Manager  S
Joined: 23 Sep 2016
Posts: 236
Re: What is the smallest possible common multiple of two integer  [#permalink]

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babusona wrote:
What is the smallest possible common multiple of two integers which are both greater than 250?

A. 251
B. 252
C. 502
D. 750
E. 884

Imo is A if this question is correct because there is nothing about those two number whether they are distinct or same.
Intern  B
Joined: 20 Dec 2017
Posts: 36
Location: Singapore
Re: What is the smallest possible common multiple of two integer  [#permalink]

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If distinct, then a=251 b=502 to achieve the smallest LCM of 502.
Since it is not mentioned that they must be distinct, the 2 integers can be the same i.e. 251

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Location: France
GMAT 1: 200 Q1 V1 GPA: 3.82
WE: Consulting (Other)
Re: What is the smallest possible common multiple of two integer  [#permalink]

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This is a problem in which it's easiest to take a step back and think about the answer choices. So we should think about how to make the common multiple the smallest if our only requirement is that both integers must be greater than 250. If both integers were 251, the smallest common multiple of these integers would be 251. Thus, Answer Choice (A) is correct.
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Intern  Joined: 01 Jul 2018
Posts: 1
What is the smallest possible common multiple of two integer  [#permalink]

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I just want to express my full admiration of your skills and effort to post all this things here

Bunuel What is the smallest possible common multiple of two integer   [#permalink] 13 Dec 2018, 07:26
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