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

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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

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

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New post 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 = \(2^2* 3 * x *y\) = \(12xy\)

Answer: Option
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Re: The positive integers p and r have exactly three prime factors in  [#permalink]

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New post 05 Jun 2015, 11:28
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the lcm = 2^2 *3 * x* y = 12xy
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Re: The positive integers p and r have exactly three prime factors in  [#permalink]

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New post 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
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The positive integers p and r have exactly three prime factors in  [#permalink]

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New post 06 Jun 2015, 09:51
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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
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Re: The positive integers p and r have exactly three prime factors in  [#permalink]

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New post 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:
Image

The correct answer is A.

Attachment:
2015-06-08_1658.png
2015-06-08_1658.png [ 33.57 KiB | Viewed 2212 times ]

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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

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

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New post 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
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Re: The positive integers p and r have exactly three prime factors in  [#permalink]

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