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If the least common multiple of positive integer z and 24 is 72...

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by swerve » Wed Mar 18, 2020 1:58 pm
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Source: e-GMAT

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

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

The OA is C
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Re: If the least common multiple of positive integer z and 24 is 72...

by Scott@TargetTestPrep » Fri Mar 20, 2020 5:58 am
swerve wrote: ↑
Wed Mar 18, 2020 1:58 pm
 Source: e-GMAT

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

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

The OA is C
Since 3 and 6 are factors of 24, then the LCM of either of them and 24 can’t be 72. We can rule out A and B as the correct answer. Now let’s look at 9. Since 9 = 3^2 and 24 = 3 x 2^3, the LCM of 9 and 24 is 3^2 x 2^3 = 8 x 9 = 72. Since 9 is a factor of 54, the GCD of 9 and 54 is 9. So z must be 9.

Answer: C

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