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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
Which of the following CANNOT be the least common multiple of two posi
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24 Sep 2022, 06:43
24 Sep 2022, 06:43
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Question Stats:
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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
(A) xy
(B) x
(C) y
(D) x - y
(E) x + y
Re: Which of the following CANNOT be the least common multiple of two posi
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25 Sep 2022, 19:00
25 Sep 2022, 19:00
Hi GeminiHeat,
Thanks for your post. I understand that D is the answer. However, can LCM be the summation of the the numbers? I cannot think of any example.
Thanks.
Thanks for your post. I understand that D is the answer. However, can LCM be the summation of the the numbers? I cannot think of any example.
Thanks.
Retired Moderator
Joined: 10 Apr 2015
Posts: 6218
Given Kudos: 136
Re: Which of the following CANNOT be the least common multiple of two posi
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25 Sep 2022, 21:19
25 Sep 2022, 21:19
2
Key Concept: the least common multiple (LCM) of x and y is a multiple of x and a multiple of y.
Let's examine a few multiples:
Multiples of 7: 7, 14, 21, 28, 35,...
Multiples of 10: 10, 20, 30, 40, 50, 60, ,...
Multiples of 3: 3, 6, 9, 12, 15, 18,,...
Notice that the multiples of N are always greater than or equal to N
So, the LCM of x and y must be greater than or equal to x AND greater than or equal to y
Answer choice D (x - y), suggests that x-y is a multiple of x and y
HOWEVER, we can see that x-y is clearly LESS THAN x
As such, x-y cannot be a multiple of x, which also means x-y cannot be the LCM of x and y
Answer: D
Cheers,
Brent
Let's examine a few multiples:
Multiples of 7: 7, 14, 21, 28, 35,...
Multiples of 10: 10, 20, 30, 40, 50, 60, ,...
Multiples of 3: 3, 6, 9, 12, 15, 18,,...
Notice that the multiples of N are always greater than or equal to N
So, the LCM of x and y must be greater than or equal to x AND greater than or equal to y
Answer choice D (x - y), suggests that x-y is a multiple of x and y
HOWEVER, we can see that x-y is clearly LESS THAN x
As such, x-y cannot be a multiple of x, which also means x-y cannot be the LCM of x and y
Answer: D
Cheers,
Brent
