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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

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by M7MBA » Tue May 12, 2020 6:40 am

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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 \(x \neq y,\) which of the following represents the least common multiple of \(p\) and \(r?\)

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

[spoiler]OA=A[/spoiler]

Source: Manhattan GMAT
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Source: — Problem Solving |

M7MBA wrote:
Tue May 12, 2020 6:40 am
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 \(x \neq y,\) which of the following represents the least common multiple of \(p\) and \(r?\)

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

[spoiler]OA=A[/spoiler]
Solution:

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

Answer: A

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