GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Oct 2019, 00:11

### 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

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

# The positive integers p and r have exactly three prime factors in

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58407
The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

04 Jun 2015, 04:29
1
00:00

Difficulty:

15% (low)

Question Stats:

77% (01:24) correct 23% (01:21) wrong based on 242 sessions

### HideShow timer Statistics

The positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y , which of the following represents the least common multiple of p and r?

(A) 12xy
(B) 6xy
(C) xy
(D) 12
(E) 6

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2978
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

04 Jun 2015, 06:19
Bunuel wrote:
The positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y , which of the following represents the least common multiple of p and r?

(A) 12xy
(B) 6xy
(C) xy
(D) 12
(E) 6

The positive integers p and r have exactly three prime factors in common: two 2's and one 3

i.e. GCD of p and r = $$2^2* 3$$

p = $$2^2* 3 * x$$
r = $$2^2* 3 * y$$

i.e. LCM of p and r = p = $$2^2* 3 * x *y$$ = $$12xy$$

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Intern
Joined: 23 Apr 2014
Posts: 20
Re: The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

05 Jun 2015, 11:28
1
the lcm = 2^2 *3 * x* y = 12xy
Manager
Joined: 18 Nov 2013
Posts: 75
Concentration: General Management, Technology
GMAT 1: 690 Q49 V34
Re: The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

06 Jun 2015, 09:09
The positive integers p and r have exactly three prime factors in common: two 2's and one 3.
$$p = 2 * 2 * 3 \\ r = 2 * 2 * 3$$

further, If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y.
$$p = 2 * 2 * 3 * x \\ r = 2 * 2 * 3 * y$$

which of the following represents least common multiple of p and r ?
LCM = highest power of all factors in both numbers , and (remember its talking about LCM )
$$LCM (p,r) = 2 * 2 * 3 * x * y = 12xy$$

Ans A
_________________
_______
- Cheers

+1 kudos if you like
Math Expert
Joined: 02 Aug 2009
Posts: 8007
The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

06 Jun 2015, 09:51
1
Bunuel wrote:
The positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y , which of the following represents the least common multiple of p and r?

(A) 12xy
(B) 6xy
(C) xy
(D) 12
(E) 6

the LCM has to have 2 of 2's, a 3 ,x and y=12xy
ans A
_________________
Math Expert
Joined: 02 Sep 2009
Posts: 58407
Re: The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

08 Jun 2015, 05:59
Bunuel wrote:
The positive integers p and r have exactly three prime factors in common: two 2's and one 3. If p has exactly one additional prime factor x and r has exactly one additional prime factor y such that x ≠ y , which of the following represents the least common multiple of p and r?

(A) 12xy
(B) 6xy
(C) xy
(D) 12
(E) 6

MANHATTAN GMAT OFFICIAL SOLUTION:

Draw overlapping circles in which to place the shared and non-shared prime factors of p and r. To find the least common multiple (LCM), multiply from left to right and include all the common factors in the product:

Attachment:

2015-06-08_1658.png [ 33.57 KiB | Viewed 2612 times ]

_________________
Manager
Joined: 19 Nov 2014
Posts: 60
Location: India
Concentration: Technology, General Management
Schools: ISB '18
WE: Information Technology (Computer Software)
The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

17 Oct 2015, 07:37
P and R have exactly 3 factors i.e. 2 , 2 and 3 which comes out to be 12 ;

so p and r wil have 12 for sure as a factor ; ok .

now considering that both p -> x as a prime factor and r-> y as prime factor and x is not equal to y ;

LCM wil be 12 * x * y

eg: -

let p and r be 12 and 12 each ; then 7 added to p and 11 added to r we get Least LCM as

12 *7* 11
_________________
KUDOS pls if you like My Post
Non-Human User
Joined: 09 Sep 2013
Posts: 13384
Re: The positive integers p and r have exactly three prime factors in  [#permalink]

### Show Tags

27 Jan 2018, 04:27
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: The positive integers p and r have exactly three prime factors in   [#permalink] 27 Jan 2018, 04:27
Display posts from previous: Sort by