Find all School-related info fast with the new School-Specific MBA Forum

It is currently 21 Aug 2014, 06:27

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If N is the least positive integer that is a multiple of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 24 Nov 2012
Posts: 12
Followers: 0

Kudos [?]: 1 [0], given: 0

If N is the least positive integer that is a multiple of [#permalink] New post 26 Nov 2012, 23:58
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

85% (01:56) correct 15% (00:59) wrong based on 33 sessions
If N is the least positive integer that is a multiple of each of the numbers 15, 18, 40, and 50, which of the following statements about N is true?

A. N <= 200
B. 200 < N <= 2,000
C. 2,000 < N <= 20,000
D. 20,000 < N <= 200,000
E. N> 200,000

Last edited by Bunuel on 27 Nov 2012, 02:08, edited 1 time in total.
Renamed the topic and edited the tags.
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19037
Followers: 3360

Kudos [?]: 24448 [1] , given: 2677

Re: If N is the least positive integer that is a multiple of [#permalink] New post 27 Nov 2012, 02:13
1
This post received
KUDOS
Expert's post
saxenarahul021 wrote:
If N is the least positive integer that is a multiple of each of the numbers 15, 18, 40, and 50, which of the following statements about N is true?

A. N <= 200
B. 200 < N <= 2,000
C. 2,000 < N <= 20,000
D. 20,000 < N <= 200,000
E. N> 200,000


Given that N is the least common multiple of 15, 18, 40, and 50.

15 = 3*5;
18 = 2*3^2;
40 = 2^3*5;
50 = 2*5^2.

N = 2^3*3^2*5^2 = 1,800.

Answer: B.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 232
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 32 [0], given: 40

Re: If N is the least positive integer that is a multiple of [#permalink] New post 20 Oct 2013, 15:07
Bunuel wrote:
saxenarahul021 wrote:
If N is the least positive integer that is a multiple of each of the numbers 15, 18, 40, and 50, which of the following statements about N is true?

A. N <= 200
B. 200 < N <= 2,000
C. 2,000 < N <= 20,000
D. 20,000 < N <= 200,000
E. N> 200,000


Given that N is the least common multiple of 15, 18, 40, and 50.

15 = 3*5;
18 = 2*3^2;
40 = 2^3*5;
50 = 2*5^2.

N = 2^3*3^2*5^2 = 1,800.

Answer: B.


Is that from some formula for LCM of a group of numbers? I'm curious as to why the 3*5 got ignored when figuring out the answer.

edit: nevermind, google is my friend.
Intern
Intern
avatar
Joined: 03 Sep 2013
Posts: 3
Location: United States
Concentration: Finance, Entrepreneurship
GMAT Date: 10-26-2013
WE: Analyst (Other)
Followers: 0

Kudos [?]: 5 [0], given: 2

Re: If N is the least positive integer that is a multiple of [#permalink] New post 20 Oct 2013, 19:59
Well for the sake of the forum, and myself, could you post why exactly 3&5 were ignored?

Posted from my mobile device Image
Manager
Manager
avatar
Joined: 26 Sep 2013
Posts: 232
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41
GMAT 2: 730 Q49 V41
Followers: 2

Kudos [?]: 32 [0], given: 40

Re: If N is the least positive integer that is a multiple of [#permalink] New post 20 Oct 2013, 20:09
ricardochavez wrote:
Well for the sake of the forum, and myself, could you post why exactly 3&5 were ignored?

Posted from my mobile device Image


To find the lowest common factor of a group of numbers, take the prime factorization of those numbers. For each prime number listed, take the most repeated occurrence of this number in any prime factorization. Then multiply them together.


15 = 3*5;
18 = 2*3^2; 3 occurs twice in 18 (3^2), it only appears one in 15.
40 = 2^3*5; 2 occurs thrice in 40, it only appears once in 18, and once in 50
50 = 2*5^2; 5 occurs twice in 50, it only appears once in 15.

So now that we see the highest power of each prime number that appears in these factorials we multiply them all together:

N = 2^3*3^2*5^2 = 1,800.
Intern
Intern
avatar
Status: Onward and upward!
Joined: 09 Apr 2013
Posts: 18
Location: United States
GMAT 1: Q V
Followers: 0

Kudos [?]: 8 [0], given: 72

Re: If N is the least positive integer that is a multiple of [#permalink] New post 21 Oct 2013, 12:51
ricardochavez wrote:
Well for the sake of the forum, and myself, could you post why exactly 3&5 were ignored?

Posted from my mobile device Image


Least Common Multiple = the smallest multiple of two or more integers.

The LCM is the lowest product for all of the shared primes.

We ignore the 3 and 5 because we are looking to find the lowest common multiple.

LCM is not to be confused with the Greatest Common Factor- which is the common factor of ALL integers. They are easily mixed up! :wink:

Now to the problem:

Step 1. List the primes for each number

15 - 5,3
18 - 3,3,2
40 - 5,2,2,2
50 - 5,5,2

Step 2. Group common multiples - those that occur the most frequent

5,5(all but 18 have at least one 5 and you must be able to solve for each number given the primes. By having two 5's, we can still solve for 50)
3,3(18 and 15 both have 3, so we need two)
2,2,2 - we need at least three 2's to account for 40. Anything else would be redundant.

Step 3:Multiply together (2^3)(5^2)(3^2) = 1800

B is the only option that fits within the perimeters.
_________________

Kudos if my post was helpful! :)

Re: If N is the least positive integer that is a multiple of   [#permalink] 21 Oct 2013, 12:51
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic Is the positive integer n a multiple of 24 ? Bunuel 6 26 Feb 2014, 01:33
Experts publish their posts in the topic Is the positive integer n a multiple of 24? Baten80 7 22 Feb 2011, 23:35
4 Experts publish their posts in the topic If the least common multiple of positive integer m and n is vd 7 12 Jun 2008, 23:09
Experts publish their posts in the topic is the positive integer n a multiple of 24? buffett76 6 22 May 2007, 09:06
If the least common multiple of distinct positive integers kevincan 7 18 Sep 2006, 05:06
Display posts from previous: Sort by

If N is the least positive integer that is a multiple of

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.