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

Question

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

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

GMATinsight · Answer

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  A

kasturi72 · Answer

the lcm = 2^2 *3 * x* y = 12xy

UJs · Answer

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

chetan2u · Answer

the LCM has to have 2 of 2's, a 3 ,x and y=12xy
ans A

Or

What is p? 
It contains two 2s, one 3 and x = 4*3*x = 12x
What is r? 
It contains two 2s, one 3 and y = 4*3*y = 12y

LCM(12x,12y) where x and y are co prime, that is they are different prime numbers. 
LCM = 12*x*y =12xy.

Bunuel · Answer

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: https://gmatclub.com/forum/download/file.php?id=26869 The correct answer is A. 2015-06-08_1658.png

rohitkumar77 · Answer

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

ScottTargetTestPrep · Answer

The LCM of p and r is 2^2 * 3 * x * y = 12xy.

Answer: A

RastogiSarthak99 · Answer

I honestly just like taking numbers.

we know that p = 12x and r = 12y and that both both an additional prime factor wherein x is not equal to y

so just taking numbers here:

12(5) and 12(7)

where x = 5 and y = 7

p = 60 and r = 84

LCM between p and r is 420

420 = 84 *5
LCM = 12(y)(x)

A

bumpbot · Answer

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

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