This one from Kaplan
If 'a' and 'b' are positive even integers, and the least common multiple of 'a' and 'b' is expressed as ab/n, which of the following could be false?
A) n is a factor of both a and b
B) ab/n < ab
C) ab is a multiple of 2
D) ab/n is a multiple of 2
E) n is a multiple of 4
This question is easier if you know that, for any positive integers a and b: LCM(a,b) * GCD(a,b) = a*b
So LCM(a,b) = ab/GCD(a,b)
In this question, n is just the GCD of a and b. So we know automatically that n is a factor of a and b... A) must be true.
If a and b are both even, they are both divisible by 2, so the smallest possible value for their GCD is 2. That is, n >= 2, so B) must be true
If a and b are even, ab is clearly even, and so is the LCM of a and b, so C) and D) must be true. E) is the only one that might be false; E will only be true if both a and b are divisible by 4.
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