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If the least common multiple of a positive integer \(z\) and 24 is 72, and the GCD of \(z\) and 54 is 9, what is the

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by Gmat_mission » Sat Jun 06, 2020 4:53 am
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If the least common multiple of a positive integer \(z\) and 24 is 72, and the GCD of \(z\) and 54 is 9, what is the value of \(z?\)

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

[spoiler]OA=C[/spoiler]

Source: e-GMAT
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Re: If the least common multiple of a positive integer \(z\) and 24 is 72, and the GCD of \(z\) and 54 is 9, what is the

by deloitte247 » Sat Jun 13, 2020 5:40 am
Given that:
LCM of z and 24 = 72
HCF or GCD of z and 54 = 9; by testing the given option:

If z = 3; LCM of 3 and 24 = 24 (not equal to 72)
HCF of 3 and 54 = 3 (not equal to 9)

If z = 6; LCM of 6 and 24 = 24 (not equal to 72)
HCF of 6 and 54 = 6 (not equal to 9)

If z = 9; LCM of 9 and 24 = 72 (equal to 72)
HCF of 9 and 54 = 9 (equal to 9)

If z = 18; LCM of 18 and 24 = 72 (equal to 72)
HCF of 18 and 54 = 18 (not equal to 9)

If z = 36; LCM of 36 and 24 = 72 (equal to 72)
HCF of 36 and 54 = 18 (not equal to 9)

The only option that satisfies the required condition is when z = 9

Answer = C
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