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# if the least common multiple of positive integer z and 24 is 72, and G

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Intern
Joined: 25 Apr 2018
Posts: 10
Location: India
Concentration: Strategy, Finance
Schools: ISB '20, SMU '21
GMAT 1: 600 Q40 V33
if the least common multiple of positive integer z and 24 is 72, and G  [#permalink]

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Updated on: 21 Apr 2019, 09:43
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Difficulty:

25% (medium)

Question Stats:

74% (01:45) correct 26% (02:18) wrong based on 23 sessions

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if the least common multiple of positive integer z and 24 is 72, and GCD of z and 54 is 9,what is value of z?

A.3
B.6
C.9
D.18
E.36

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Originally posted by axezcole on 21 Apr 2019, 09:08.
Last edited by Bunuel on 21 Apr 2019, 09:43, edited 1 time in total.
Renamed the topic and edited the question.
Senior Manager
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Location: India
Concentration: General Management, Finance
GMAT 1: 720 Q50 V37
WE: Information Technology (Computer Software)
Re: if the least common multiple of positive integer z and 24 is 72, and G  [#permalink]

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21 Apr 2019, 09:43
1
Given that,
LCM z and 24 = 72
GCD of z and 54 = 9

Condition 1: LCM z and 24 = 72
24 = $$2^{3} 3^{1}$$
72 = $$2^{3} 3^{2}$$
Therefore, z = $$3^{2}$$, $$2^{1} 3^{2}$$, $$2^{2} 3^{2}$$, or $$2^{3} 3^{2}$$, i.e. four possible values. For each of these 4 values of z and 24, the LCM is 72.

Condition 2: GCD of z and 54 = 9
54 = $$2^{1} 3^{3}$$
9 = $$3^{2}$$
Therefore, z = $$3^{2}$$ x Muliple of any Prime number except 2.

From conditions 1 and 2, we get a unique value of z, i.e.z = $$3^{2}$$

Hence, the correct answer is option C. 9

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Manager
Joined: 12 Sep 2017
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if the least common multiple of positive integer z and 24 is 72, and G  [#permalink]

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21 Apr 2019, 18:14
1

LCM of 9 and 24 is 72.

GDF of 9 and 54:

54: 1 2 3 6 9 18 27 54
9: 1, 3, 9

C
Math Expert
Joined: 02 Aug 2009
Posts: 7688
Re: if the least common multiple of positive integer z and 24 is 72, and G  [#permalink]

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21 Apr 2019, 19:01
2
1
axezcole92 wrote:
if the least common multiple of positive integer z and 24 is 72, and GCD of z and 54 is 9,what is value of z?

A.3
B.6
C.9
D.18
E.36

Just one line will eliminate all choices..

GCD of z and 54 is 9.
This tells you two things..
(i) z is a multiple of 9 but not of 27 as 54 contains a 27 in it......Only C, D and E are left
(ii) z is not even as 54 contains a 2 in it... Only A and C are left

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Re: if the least common multiple of positive integer z and 24 is 72, and G   [#permalink] 21 Apr 2019, 19:01
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