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The greatest common factor of 36, 54, and 90
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09 Aug 2022, 06:41
09 Aug 2022, 06:41
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Question Stats:
45% (00:59) correct
55% (01:20) wrong based on 20 sessions
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Quantity A |
Quantity B |
The greatest common factor of 36, 54, and 90 |
least common multiple of 18, 3, and 6 |
A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given
Part of the project: GRE QCQ & PS 3 Questions Every One DAILY Challenge - (2022)
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GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
GRE Math Essentials (2022)
GRE Geometry Formulas
GRE - Math Book
Re: The greatest common factor of 36, 54, and 90
[#permalink]
10 Aug 2022, 05:42
10 Aug 2022, 05:42
Solution -
Quantity A - The greatest common factor of 36, 54, and 90
36 = (3)^2 * (2)^2
54 = (3)^3 * (2)^1
90 = (3)^2 * (5)^1 * (2)^1
GCF = (3)^2 * (2)^1 = 9 * 2 = 18
Quantity B - The least common multiple of 18, 3, and 6
18 = (3)^2 * (2)^1
3 = (3)^1 * (1)^1
6 = (3)^1 * (2)^1
LCM = (3)^2 * (2)^1 = 9 * 2 = 18
Hence, Quantity A = Quantity B
Correct Answer Choice is C
Quantity A - The greatest common factor of 36, 54, and 90
36 = (3)^2 * (2)^2
54 = (3)^3 * (2)^1
90 = (3)^2 * (5)^1 * (2)^1
GCF = (3)^2 * (2)^1 = 9 * 2 = 18
Quantity B - The least common multiple of 18, 3, and 6
18 = (3)^2 * (2)^1
3 = (3)^1 * (1)^1
6 = (3)^1 * (2)^1
LCM = (3)^2 * (2)^1 = 9 * 2 = 18
Hence, Quantity A = Quantity B
Correct Answer Choice is C
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Re: The greatest common factor of 36, 54, and 90
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28 Oct 2022, 07:40
28 Oct 2022, 07:40
Quantity A: The greatest common factor of 36, 54, and 90
36 = 4*9 = \(2^2 * 3^2\)
54 = 6*9 = \(2^1 * 3^3\)
90 = 9*10 = \(2^1 * 3^2 * 5^1\)
To find the GCD take all the common terms and take their lowest power in all of the above.
=> GCD(36,54,90) = \(2^1 * 3^2\) = 18
Quantity B: The least common multiple of 18, 3 and 6
18 = 2*9 = \(2^1 * 3^2\)
3 = \(3^1\)
6 = 2*3 = \(2^1 * 3^1\)
To find the LCM take all the terms and take their highest power in all of the above.
=> LCM(18,3,6) = \(2^1 * 3^2\) = 18
Clearly, Quantity A = Quantity B = 18
So, Answer will be C
Hope it helps!
To learn more about LCM and GCD watch the following videos
36 = 4*9 = \(2^2 * 3^2\)
54 = 6*9 = \(2^1 * 3^3\)
90 = 9*10 = \(2^1 * 3^2 * 5^1\)
To find the GCD take all the common terms and take their lowest power in all of the above.
=> GCD(36,54,90) = \(2^1 * 3^2\) = 18
Quantity B: The least common multiple of 18, 3 and 6
18 = 2*9 = \(2^1 * 3^2\)
3 = \(3^1\)
6 = 2*3 = \(2^1 * 3^1\)
To find the LCM take all the terms and take their highest power in all of the above.
=> LCM(18,3,6) = \(2^1 * 3^2\) = 18
Clearly, Quantity A = Quantity B = 18
So, Answer will be C
Hope it helps!
To learn more about LCM and GCD watch the following videos
