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# What is the smallest possible common multiple of two integer

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What is the smallest possible common multiple of two integer [#permalink]

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08 Apr 2012, 13:12
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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
[Reveal] Spoiler: OA
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Re: What is the smallest possible common multiple of two integer [#permalink]

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08 Apr 2012, 13:40
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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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21 Dec 2012, 04:49
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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27 May 2013, 13:30
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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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Re: What is the smallest possible common multiple of two integer [#permalink]

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27 May 2013, 13:36
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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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Re: What is the smallest possible common multiple of two integer [#permalink]

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13 Jun 2013, 06:10
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!
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Re: What is the smallest possible common multiple of two integer [#permalink]

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13 Jun 2013, 06:19
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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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Re: What is the smallest possible common multiple of two integer [#permalink]

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19 Dec 2013, 03:06
Bunuel, can you please suggest some other/similar questions that are testing this topic? Thank you.
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19 Dec 2013, 07:15
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15 Jun 2015, 11:14
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Re: What is the smallest possible common multiple of two integer [#permalink]

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31 Jan 2016, 22:34
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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18 Jul 2016, 20:11
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?
Re: What is the smallest possible common multiple of two integer   [#permalink] 18 Jul 2016, 20:11
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# What is the smallest possible common multiple of two integer

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