How many 4-digit positive integers are multiple of each integer from

didnt get u.....pls elaborate

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.

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.

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.

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.

Hope it's clear.

Bunuel, awesome answer... Can you please check my post on combinations and answer it when you have a chance.. Thanks

Posted from my mobile device

Find LCM of nos between 1 & 10
which also means just LCM of 7,8,9 & 10 (As all smaller are multiple of these)

Just 2 is repeated once, else all are unique

7*8*9*5 = 63*40 = 2520

2520, 2520+2520, 2520+2520+2520 is the answer

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

Least No which could be divisible by integers [ 1,2,3,4,5,6,7,8,9,10] is the LCM of the said integers.

LCM [1,2,3,4,5,6,7,8,9,10] = 2520

No the Nos which are divisible by 2520 will be divisible by [1,2,3,4,5,6,7,8,9]

There are 3 values possible between 1000 to 9999

They are 2520 x 1= 2520
2520 x 2 = 5040
2520 x 3 = 7560

7*8*9*10=5040
5040/2=2520
2520*3=7560
3

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.