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# What is the lowest possible common multiple of 2 distinct integers

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What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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23 Oct 2016, 08:26
1
9
00:00

Difficulty:

55% (hard)

Question Stats:

56% (01:21) correct 44% (01:19) wrong based on 161 sessions

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What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68
B. 69
C. 136
D. 68^2
E. 68·69

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Re: What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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25 Oct 2016, 03:32
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3
Bunuel wrote:
What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68
B. 69
C. 136
D. 68^2
E. 68·69

Here is a useful train of thought:
The numbers need to be > 67 and distinct.
The first smallest such number would be 68.
The LCM cannot be 68 since the second number needs to be > 67 too and distinct. So the LCM would contain all factors of 68 and another factor other than 1.
The smallest factor other than 1 is 2.
So the LCM should be 68*2 = 136
This means the second number must be 136 (though that is immaterial).

Any other pair such as 68 and 69 would involve LCM getting 68 and many factors more than 2.

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What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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23 Oct 2016, 08:43
Bunuel wrote:
What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68
B. 69
C. 136
D. 68^2
E. 68·69

in order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.

So, I can take 68 and 136 as two distinct numbers, such that Lowest LCM = 136.
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What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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23 Oct 2016, 11:38
abhimahna wrote:
Bunuel wrote:
What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68
B. 69
C. 136
D. 68^2
E. 68·69

in order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.

So, I can take 68 and 136 as two distinct numbers,such that Lowest LCM = 68.

abhimahna

Lcm of 68 &136=136
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Re: What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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23 Oct 2016, 12:30
1
Bunuel wrote:
What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68
B. 69
C. 136
D. 68^2
E. 68·69

The question asks the LCM of 2 numbers > 67 ( ie, 68, 69 ,70........................)

Try with the first one 68*69 => 4692 ( Option E )

But, can we have any other pair giving LCM less than 68*69 ?

Yes , we can if we consider one of the 2 numbers as a multiple of the other Number..

So, Let the numbers be 68 & 136

Hence , LCM of 68 & 136 is 136 < The LCM of 68 & 69

So, Correct answer will be (C)

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Re: What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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23 Oct 2016, 19:49
rohit8865 wrote:
abhimahna wrote:
Bunuel wrote:
What is the lowest possible common multiple of 2 distinct integers, each greater than 67?

A. 68
B. 69
C. 136
D. 68^2
E. 68·69

in order to get the lowest LCM, we have to take the first number as 68 and the next number as its multiple.

So, I can take 68 and 136 as two distinct numbers,such that Lowest LCM = 68.

abhimahna

Lcm of 68 &136=136

Ohh yeah, made a silly mistake. Corrected the solution now. Thanks
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Re: What is the lowest possible common multiple of 2 distinct integers  [#permalink]

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05 Nov 2017, 10:07
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Re: What is the lowest possible common multiple of 2 distinct integers &nbs [#permalink] 05 Nov 2017, 10:07
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