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If r and s are positive integers, is the least common multiple of r an

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Math Revolution GMAT Instructor
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If r and s are positive integers, is the least common multiple of r an  [#permalink]

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New post 04 Jan 2017, 05:14
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If r and s are positive integers, is the least common multiple of r and s equal to the product of r and s?

1) r and s are consecutive odd numbers
2) r=s+2

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Re: If r and s are positive integers, is the least common multiple of r an  [#permalink]

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New post 04 Jan 2017, 08:08
MathRevolution wrote:
If r and s are positive integers, is the least common multiple of r and s equal to the product of r and s?

1) r and s are consecutive odd numbers
2) r=s+2



LCM of two numbers is equal to the product of that two numbers when the two numbers don't share any common prime factors.
Given that r and s are positive integers .

statement 1 : r and s are consecutive odd integers . As consecutive odd integers don't share any common prime factors. We can be sure that LCM will be equal to the product of that two numbers .
Statement 1 is sufficient .
Ex. 3 and 5 / 21 and 23 / 97 and 99 etc .

statement 2, r = s +2
r can be 8 and s can be 6 : in this case the LCM is not equal to product (LCM = 24 and product = 48 )
or
r can be 5 and s can be 3 : in this case the LCM = product = 15


Answer is A .
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Re: If r and s are positive integers, is the least common multiple of r an  [#permalink]

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New post 06 Jan 2017, 02:39
==> In the original condition, there are 2 variables (r, s), and therefore C is most likely to be the answer. By solving con 1) and con 2), it is yes, hence sufficient. Therefore, C is the answer. However, since it is an integer question, one of the key questions, if you apply CMT 4(A) on con 1), you get yes and hence it is sufficient.

Therefore, the answer is A.
Answer: A
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Re: If r and s are positive integers, is the least common multiple of r an  [#permalink]

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New post 09 May 2017, 16:42
sb0541 wrote:
consecutive odd integers don't share any common prime factors


Wish I had known this, I would have been able to solve the problem
Re: If r and s are positive integers, is the least common multiple of r an &nbs [#permalink] 09 May 2017, 16:42
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