Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

I am going to assume that you mean 1 to 10 inclusive.

If you wanted to know if a number was divisible by all those digits, you would have to find the smallest # that was divisible by 1 through 10.

1- Every # from 1000 to 9999 1 to 2 - Every even number 1 to 3 - Every multiple of 6 from 1000 to 9999 1 to 4 - Every multiple of 12 from 1000 to 9999 1 to 5 - Every multiple of 60 From 1000 to 9999 1 to 6 - Every multiple of 60 from 1000 to 9999 1 to 7 - Every multiple of 210 from 1000 to 9999 1 to 8 - Every multiple of 840 from 1000 to 9999 1 to 9 - Every multiple of 2520 from 1000 to 9999 1 to 10 - Every multiple of 2520 from 1000 to 9999

With that said, there are three 4-digit numbers that satisfy the requirements of being divisible by 1 through 10 inclusive.

If you mean you didn't get my response. Here is the breakdown:

To get a number that is divisible by all 10 numbers you could do 10!. But 10! = 3628800 and it is not the lower common multiple. To get the LCM, I took all the numbers like this: 1 X 2 X 3 X 4 X 5 X 6 X 7 X 8 X 9 X 10. I removed the 6, 8, 9, 10 and added a 3. I ended up with 1 X 2 X 3 X 3 X 4 X 5 X 7 which equals 2520 I removed the 6 because it is a multiple of 2 and 3 earlier in the list. I removed the 8 because it is a multiple of 2 and 4 earlier in the list. I removed the 10 because it is a multiple of 2 and 5 earlier in the list. For the 9 to be removed, you needed two 3's. So I added a 3 and removed the 9.

With those adjustments I came up with 2520 as the lowest common multiple for integers from 1 to 10.

Because the question asked between the range of 1000 and 9999, three numbers satisfy the requirements: 2520, 5040, 7560.

Finding the lowest common multiple can be a little confusing. I didn't know how to calculate it so I had to work out how to do this on a smaller subset. I used the one through five range to figure how to figure out the LCM.

how many 4-digit positive integers are multiple of each integer from 1 to 10

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is \(2^3*3^2*5*7=2520\).

There are 3 such numbers: 2520, 5040, and 7560.
_________________

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is .

There are 3 such numbers: 2520, 5040, and 7560.

lecancher wrote:

Hi,

Can anyone help me with this pls?

how many 4-digit positive integers are multiple of each integer from 1 to 10

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is \(2^3*3^2*5*7=2520\).

There are 3 such numbers: 2520, 5040, and 7560.

Fabulous approach and solution.

Just goes to show that no matter how much you go when you first read a question that there is almost always a shorter route to the answer, if you are clever enough.
_________________

Just goes to show that no matter how much you go when you first read a question that there is almost always a shorter route to the answer, if you are clever enough.

You nailed the secret to approach GMAT!!! In fact, you are already a Manager. Focus, problem, possibilities and solution, that is all it is in that big bad corporate world. Double Hi Fives bro!!!
_________________

You nailed the secret to approach GMAT!!! In fact, you are already a Manager. Focus, problem, possibilities and solution, that is all it is in that big bad corporate world. Double Hi Fives bro!!!

Let's meet up at MacLaren's after work for a pint, we can discuss how we gon run dis town after we takeover.
_________________

how many 4-digit positive integers are multiple of each integer from 1 to 10

4-digit positive integer should be multiple of: 2, 3, 4(=2^2), 5, 6(=2*3), 7, 8(=2^3), 9(=3^2), 10(=2*5). Basically our 4-digit integer should be multiple of LCM of these numbers, which is \(2^3*3^2*5*7=2520\).

There are 3 such numbers: 2520, 5040, and 7560.

Hi Bunuel,

Can you please explain how did you get the other 2 nos - 5040 and 7560?

Many thnx

The least 4-digit number which is multiple of each integer from 1 to 10 is LCM of these numbers and equals to \(2^3*3^2*5*7=2520\).

Now, if we multiply this number by 2 and 3 we will still have 4-digit number which is multiple of each integer from 1 to 10 --> \(2520*2=5040\) and \(2520*3=7560\) (if we multiply by 4 the number will be 5-digit). So there are only 3 such numbers.

Re: How many 4-digit positive integers are multiple of each inte [#permalink]

Show Tags

11 Feb 2014, 06:19

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: How many 4-digit positive integers are multiple of each inte [#permalink]

Show Tags

24 Mar 2015, 06:35

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: How many 4-digit positive integers are multiple of each inte [#permalink]

Show Tags

08 May 2016, 05:35

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Re: How many 4-digit positive integers are multiple of each inte [#permalink]

Show Tags

13 Aug 2017, 08:41

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

Version 8.1 of the WordPress for Android app is now available, with some great enhancements to publishing: background media uploading. Adding images to a post or page? Now...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...