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The least common multiple of 22 and 6

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sandy
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The least common multiple of 22 and 6 [#permalink] New post   12 Aug 2018, 15:56
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Quantity A
Quantity B
The least common multiple of 22 and 6
The greatest common factor of 66 and 99


A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
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A
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sandy
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Re: The least common multiple of 22 and 6 [#permalink] New post   15 Aug 2018, 05:10
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Explanation

The least common multiple of 22 and 6 is 66. One way to find the least common multiple is to list the larger number’s multiples (it is more efficient to begin with the larger number) until reaching a multiple that the other number goes into. The multiples of 22 are 22, 44, 66, 88, etc. The smallest of these that 6 goes into is 66.


The greatest common factor of 66 and 99 is 33. One way to find the greatest common factor is to list all the factors of one of the numbers, and then pick the greatest one that also goes into the other number. For instance, the factors of 66 are 1 & 66, 2 & 33, 3 & 22, and 6 & 11. The greatest of these that also goes into 99 is 33.

Thus, Quantity A is greater.
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Re: The least common multiple of 22 and 6 [#permalink] New post   27 Oct 2022, 10:34
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Quantity A: The least common multiple of 22 and 6

22 = 2*11 = \(2^1 * 11^1\)
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(22,6) = \(2^1 * 11^1 * 3^1\) = 66

Quantity B: The greatest common divisor of 66 and 99

66 = 2*3*11 = \(2^1 * 3^1 * 11^1\)
99 = 9*11 = \(3^2 * 11^1\)

To find the GCD take all the common terms and take their lowest power in all of the above.

=> GCD(66,99) = \(3^1 * 11^1\) = 33

Clearly, Quantity A(66) > Quantity B(33)

So, Answer will be A
Hope it helps!

To learn more about LCM and GCD watch the following videos



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The least common multiple of 22 and 6 [#permalink] New post   26 Feb 2024, 02:57
Quantity A

The LCM of 22 and 6

Multiples of 6 = 6, 12, 18, 24, 30, 36, 42, 48, 54, 60, 66, 72,
Multiples of 22 = 22, 44, 66, 88

=> 66

Quantity B

The GCF/HCF/GCD of 66 and 99

Factors of 66 = 2, 3, 11, 6, 22, 33
Factors of 99 = 3, 3, 11, 9, 33

=> 33

Quantity A is always greater.
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The least common multiple of 22 and 6 [#permalink]
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