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

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

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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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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 = $$2^2* 3 * x *y$$ = $$12xy$$

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

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1
the lcm = 2^2 *3 * x* y = 12xy
Manager  Joined: 18 Nov 2013
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GMAT 1: 690 Q49 V34 Re: The positive integers p and r have exactly three prime factors in  [#permalink]

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

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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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Math Expert V
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Posts: 58407
Re: The positive integers p and r have exactly three prime factors in  [#permalink]

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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

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: The correct answer is A.

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

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

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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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_________________ Re: The positive integers p and r have exactly three prime factors in   [#permalink] 27 Jan 2018, 04:27
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