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Which of the following CANNOT be the least common multiple of two posi

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Which of the following CANNOT be the least common multiple of two posi [#permalink]

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New post 09 Sep 2014, 02:09
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Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) xy
(B) x
(C) y
(D) x - y
(E) x + y
Spoiler: OA

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Re: Which of the following CANNOT be the least common multiple of two posi [#permalink]

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New post 09 Sep 2014, 07:10
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PareshGmat wrote:
Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) xy
(B) x
(C) y
(D) x - y
(E) x + y

Should be very easy...... :)


The least common multiple of two positive integers cannot be less than either of them. Therefore, since x - y is less than x, it cannot be the LCM of a x and y.

Answer: D.

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Re: Which of the following CANNOT be the least common multiple of two posi [#permalink]

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New post 17 Jan 2016, 21:24
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Hi All,

This question is really just a test of your overall understanding of the concept of 'least common multiple.' You don't have to do any fancy math to get the correct answer (and the design of the answer choices helps to avoid a certain amount of thinking/work).

The Least Common Multiple between two integers is the smallest number that is a positive multiple of BOTH integers.

For example:

The LCM of 2 and 3 is 6
The LCM of 2 and 4 is 4
The LCM of 3 and 5 is 15

Notice how the LCM is ALWAYS greater than OR equal to both of the integers involved. Knowing THAT rule, you can quickly deduce which answer choice CANNOT be the LCM of 2 distinct positive integers....

Final Answer:
Spoiler: ::
D


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Re: Which of the following CANNOT be the least common multiple of two posi [#permalink]

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New post 29 Apr 2017, 17:18
LCM must be greater than or equal to all the involved numbers.
Hence LCM can never be x-y as it is less than x.

Additionally => LCM(x,y) for x>y must lie in the bound => [ x,x*y]


Smash that D
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Re: Which of the following CANNOT be the least common multiple of two posi [#permalink]

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New post 26 Feb 2018, 10:58
PareshGmat wrote:
Which of the following CANNOT be the least common multiple of two positive integers x and y?

(A) xy
(B) x
(C) y
(D) x - y
(E) x + y


Since the difference of x - y is less than x, the quantity x - y can’t be a multiple of x. Thus, it can’t be the least common multiple (LCM) of x and y.

(Note: We think the correct answer is intended to be D for the reason stated above, but choice E is also correct since x + y can’t be the LCM of x and y either. We can prove this by contradiction:

Let’s suppose that x + y is the LCM of x and y. We see that x and y can’t be equal, otherwise either x or y (not their sum) will be the LCM of x and y. Now let’s say that x < y. Since we suppose that x + y is the LCM of x and y, y, the larger of the two numbers, can’t be the LCM of x and y. But the LCM of x and y must be the a multiple of y, so it has to be at least 2y (if it can’t be y). Here is the contradiction: 2y > x + y since y > x. So it’s impossible to have x + y as the LCM of x and y.)

Answer: D
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Re: Which of the following CANNOT be the least common multiple of two posi   [#permalink] 26 Feb 2018, 10:58
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