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Question

What is the least positive integer that is divisible by each of the integers 1 through 7, inclusive?

A. 420
B. 840
c. 1260
D. 2520
E. 5040

Please break this down. I feel slow attempting this kind of problem

Bullzi · Answer

Hello,
This is how I could approach, I'll let the experts confirm if this approach is right..

The first thing I noticed is that Option B through E are all multiples of option A. So, if option A is divisible by all integers 1 through 7, that should be the least positive integer divisible by each of the integers 1 through 7
I did a quick check if it is divisible and it is. So, I'll go with Option A

Thanks
Bullzi

sandipgumtya · Answer

This qus is basically asking LCM of 1,2,3,4,5,6,7.Which is 420. So I think ans is A Pl let us know the OA. Sandip.

Rich.C@EMPOWERgmat.com · Answer

Hi oquiella,

This is a great question to TEST THE ANSWERS on, but you have to pay careful attention to what is asked for: we're asked for the LOWEST integer that is divisible by all of those integers. As such, you should NOT start with Answer B or D - you should start with Answer A. If "A" is not correct, then you TEST B, and so on. There is a Number Property rule that you can use to help you to avoid some of the 'excess math.'

Any number that is divisible by 6 is ALSO divisible by 2 and 3

So, how long would it take you to determine if 420 is divisible by 7, 5, 4 and 6 (or 3 and 2)?

Final Answer: A

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

oquiella · Answer

Rich.C@EMPOWERgmat.com wrote:Hi oquiella, This is a great question to TEST THE ANSWERS on, but you have to pay careful attention to what is asked for: we're asked for the LOWEST integer that is divisible by all of those integers. As such, you should NOT start with Answer B or D - you should start with Answer A. If "A" is not correct, then you TEST B, and so on. There is a Number Property rule that you can use to help you to avoid some of the 'excess math.' Any number that is divisible by 6 is ALSO divisible by 2 and 3 So, how long would it take you to determine if 420 is divisible by 7, 5, 4 and 6 (or 3 and 2)? Final Answer: A GMAT assassins aren't born, they're made, Rich Hi there Im a little confused here...."we're asked for the LOWEST integer that is divisible by all of those integers. As such, you should NOT start with Answer B or D - you should start with Answer A." Why not start with B or D. D is quite large and B is only a little smaller. Can you further explain why you eliminated those first?

Rich.C@EMPOWERgmat.com · Answer

Hi oquiella,

I didn't eliminate Answers B and D; I chose not to start with those answers because the prompt asked for the LEAST positive integer that is divisible by 1 through 7, inclusive. If you start by TESTing Answer B and you find that it's divisible by 1 through 7 (which it IS), you won't know if it's actually the smallest integer or not UNTIL you TEST Answer A.

That would be a LOT of excessive work if it turns out that Answer A is the correct answer.

GMAT assassins aren't born, they're made,
Rich

Contact Rich at [email protected]

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