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How many 4digit positive integers are multiple of each inte [#permalink]
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09 Mar 2010, 07:07
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How many 4digit positive integers are multiple of each integer from 1 to 10



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Re: Hi! Math question [#permalink]
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09 Mar 2010, 11:32
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 4digit numbers that satisfy the requirements of being divisible by 1 through 10 inclusive.



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Re: Hi! Math question [#permalink]
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09 Mar 2010, 12:59
didnt get u.....pls elaborate
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Re: Hi! Math question [#permalink]
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09 Mar 2010, 17:33
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.



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Re: Hi! Math question [#permalink]
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10 Mar 2010, 03:06
lecancher wrote: Hi,
Can anyone help me with this pls?
how many 4digit positive integers are multiple of each integer from 1 to 10 4digit 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 4digit 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.
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Re: Hi! Math question [#permalink]
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10 Mar 2010, 14:07
gnus wrote: 4digit 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 4digit 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 4digit positive integers are multiple of each integer from 1 to 10 4digit 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 4digit 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.
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Re: Hi! Math question [#permalink]
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10 Mar 2010, 19:43
TheSituation wrote: 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!!!
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Re: Hi! Math question [#permalink]
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11 Mar 2010, 08:18
BarneyStinson wrote: 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.
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Re: Hi! Math question [#permalink]
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09 Aug 2010, 03:56
oldstudent wrote: Bunuel wrote: lecancher wrote: Hi,
Can anyone help me with this pls?
how many 4digit positive integers are multiple of each integer from 1 to 10 4digit 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 4digit 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 4digit 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 4digit 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 5digit). So there are only 3 such numbers. Hope it's clear.
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Re: Hi! Math question [#permalink]
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09 Aug 2010, 13:51
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
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Re: How many 4digit positive integers are multiple of each inte [#permalink]
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05 Mar 2014, 02:18
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
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Re: How many 4digit positive integers are multiple of each inte [#permalink]
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22 May 2016, 07:54
How many 4digit 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



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