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 statements could be false ?
1. n is a factor of both a and b
2. ab/n < ab
3. ab is multiple of 2.
4. ab/n is a multiple of 2.
5. n is a multiple of 4.
OA is 5
if a and b are positive even integers, and the least common
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This question is easier if you know that, for any positive integers a and b:airan wrote: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 statements could be false ?
1. n is a factor of both a and b
2. ab/n < ab
3. ab is multiple of 2.
4. ab/n is a multiple of 2.
5. n is a multiple of 4.
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 (I'd add, in response to reachac's comment above, we do not need to have <= here). 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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