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If a and b are positive integers and their LCM is c. Which of the following...

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by BTGmoderatorLU » Mon Apr 13, 2020 4:43 pm

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Difficulty—

Source: e-GMAT

If a and b are positive integers and their LCM is c. Which of the following cannot be the value of c?

A. a
B. b
C. a/b
D. a x b
E. a-b

The OA is E
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Re: If a and b are positive integers and their LCM is c. Which of the following...

by Jay@ManhattanReview » Thu Apr 16, 2020 12:45 am
BTGmoderatorLU wrote: ↑
Mon Apr 13, 2020 4:43 pm
 Source: e-GMAT

If a and b are positive integers and their LCM is c. Which of the following cannot be the value of c?

A. a
B. b
C. a/b
D. a x b
E. a-b

The OA is E
Let's take each option one by one.

A. a: Say a = 2 and b = 1, then c = 2 = a. The value of c can be a.

B. b: Say a = 1 and b = 2, then c = 2 = b. The value of c can be b.

C. a/b: Say a = 2 and b = 1, then c = 2 = a/b. The value of c can be a/b.

D. a x b: Say a = 2 and b = 1, then c = 2 = a x b. The value of c can be a x b.

E. a – b: This is the correct answer. Since a and b are positive integers, the LCM = c must also be positive; thus, for a – b to be the LCM, a > b. For a > b, even if b is a factor of a, the minimum value of LCM would be a.

The correct answer: E

Hope this helps!

-Jay
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Re: If a and b are positive integers and their LCM is c. Which of the following...

by Scott@TargetTestPrep » Fri Apr 17, 2020 10:51 am
BTGmoderatorLU wrote: ↑
Mon Apr 13, 2020 4:43 pm
 Source: e-GMAT

If a and b are positive integers and their LCM is c. Which of the following cannot be the value of c?

A. a
B. b
C. a/b
D. a x b
E. a-b

The OA is E
Since the LCM of two positive integers must be at least the larger of the two integers, we see that a - b can’t be the LCM of a and b, i.e., a - b can’t be the value of c.

Answer: E

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