What is the $LCM$ of $x$ and $12?$

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Vincen: Legendary Member; Posts: 2898; Joined: Thu Sep 07, 2017 2:49 pmFollowed by: 5 members; Thanked: 6 times

by Vincen » Thu Jul 30, 2020 8:30 am

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What is the $LCM$ of $x$ and $12?$

(1) The Least Common Multiple of $x$ and $9$ is $45?$
(2) The Least Common Multiple of $x$ and $4$ is $20?$

[spoiler]OA=B[/spoiler]

Source: Manhattan GMAT

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Source: Beat The GMAT — Data Sufficiency | Thu Jul 30, 2020 8:30 am

terminator12: Junior | Next Rank: 30 Posts; Posts: 13; Joined: Tue Jul 28, 2020 9:01 pm

Re: What is the $LCM$ of $x$ and $12?$

by terminator12 » Thu Jul 30, 2020 7:20 pm

Statement 1:
45 = ${3^2}$*5
9 = ${3^2}$
Hence, x = 5*${3^a}$
where a = 0, 1 ,2
x can be 5, 15, 45
Hence, this statement is insufficient.

Statement 2:
20 = ${2^2}$*5
4 = ${3^2}$
Hence, x = 5*${2^a}$
where a = 0, 1 ,2
x can be 5, 10, 20
Hence, this statement is insufficient.

Combining both statements, we get x = 5
Hence, answer should be C.

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