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# Ok, this is probably really easy, but i do not understand

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Manager
Joined: 08 Sep 2006
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Ok, this is probably really easy, but i do not understand [#permalink]  25 Apr 2007, 08:18
Ok, this is probably really easy, but i do not understand the explanation from the OG 10. It's problem solving #417 on page 131.

Question:

Which of the following is the least positive integer that is divisible by 2,3,4,5,6,7,8,and 9 ?

A) 15,120
B) 3,024
C) 2,520
D) 1,890
E) 1,680

The answer is C), but can someone please explain in your own words how to do this problem.

Thanks
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Current Student
Joined: 22 Apr 2007
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Out of all the numbers given, 9, 8, 7 and 5 have no common factor. Other numbers are factors of one of these (Like, 4 and 2 are factors of 8).

So, just multiply 9, 8, 7 and 5 and you'll get the smallest number that's a multiple of 2...9

9 x 8 x 7 x 5 = 2520

Last edited by mNeo on 25 Apr 2007, 12:43, edited 1 time in total.
Director
Joined: 18 Jul 2006
Posts: 531
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tinman1412 wrote:
Ok, this is probably really easy, but i do not understand the explanation from the OG 10. It's problem solving #417 on page 131.

Question:

Which of the following is the least positive integer that is divisible by 2,3,4,5,6,7,8,and 9 ?

A) 15,120
B) 3,024
C) 2,520
D) 1,890
E) 1,680

The answer is C), but can someone please explain in your own words how to do this problem.

Thanks

All answer choices but B ends with "0", so can't be divided by 3, 7, 9.
Current Student
Joined: 22 Apr 2007
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Juaz wrote:
All answer choices but B ends with "0", so can't be divided by 3, 7, 9.

What??? 7x9x10 = 630 is divisible by 3,7 and 9 and ends with '0'
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Break down the numbers to their primes.

Starting with C -->
2520
= 252*10
= 2*126*2*5
= 2*2*63*2*5
= 2*2*3*21*2*5
= (2^3)*(3^2)*5*7 --> divisible by 2,3,4,5,6,7,8 and 9

(Note: I started with C because 2520 is in the middle of the 5 numbers. If it's incorrect, I just need to adjust up or down.)

An example why the rest don't work. Using E, 1680, the prime factorization comes up to:
1680
= 168*10
= 4*42*2*5
= (2^3)*21*5
= (2^3)*3*5*7 <-- can't divide by 9
Manager
Joined: 18 Apr 2007
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ywilfred,

Thank you! I was just about to write a really silly question, but you answered it with your really excellent explanation. Thanks again!

Bluebird
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