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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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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
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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.

Answer: A.
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What is the smallest common multiple of two integers which [#permalink]

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New post 21 Dec 2012, 05:49
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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New post 27 May 2013, 14:30
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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.

Answer: A.


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

Answer: A.


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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New post 13 Jun 2013, 07:10
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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New post 13 Jun 2013, 07:19
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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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New post 19 Dec 2013, 04:06
Bunuel, can you please suggest some other/similar questions that are testing this topic? Thank you.

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

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New post 19 Dec 2013, 08:15
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mywaytomba wrote:
Bunuel, can you please suggest some other/similar questions that are testing this topic? Thank you.


Somewhat similar questions:
what-is-the-greatest-common-factor-of-positive-integers-a-126637.html
what-is-the-greatest-common-factor-of-x-and-y-109273.html
what-is-the-greatest-common-divisor-of-positive-integers-m-129802.html
x-and-y-are-positive-integers-such-that-x-8y-12-what-is-the-126743.html
gcd-of-a-b-126427.html
if-a-and-b-are-positive-integers-divisible-by-6-is-6-the-100324.html
if-a-and-b-are-positive-itegers-what-is-the-value-of-a-b-135199.html
is-x-1-a-factor-of-100740.html
find-the-number-that-divides-103251.html
if-n-is-the-least-of-3-consecutive-positive-integers-and-128102.html
if-x-and-y-are-positive-integers-what-is-the-gcf-of-x-and-y-144190.html
if-x-and-y-are-positive-integers-what-is-the-value-of-xy-95872.html

Hope this helps.
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Re: What is the smallest possible common multiple of two integer [#permalink]

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New post 31 Jan 2016, 23:34
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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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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New post 18 Oct 2017, 10:16
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.

Answer: A.


But we ain't even told that the numbers are same! :roll: :roll:

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

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New post 18 Oct 2017, 10:53
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.

Answer: A.


But we ain't even told that the numbers are same! :roll: :roll:


The point is that they could be the same and in this case we get the smallest possible common multiple.
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PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

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Re: What is the smallest possible common multiple of two integer   [#permalink] 18 Oct 2017, 10:53
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