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The least common multiple of 6 and 10

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Carcass
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The least common multiple of 6 and 10 [#permalink] New post   31 Dec 2021, 07:15
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Quantity A
Quantity B
The least common multiple of 6 and 10
The greatest common divisor of 80 and 140




The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given
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A
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GreenlightTestPrep
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Re: The least common multiple of 6 and 10 [#permalink] New post   31 Dec 2021, 07:40
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Carcass wrote:
Quantity A
Quantity B
The least common multiple of 6 and 10
The greatest common divisor of 80 and 140




The quantity in Column A is greater
The quantity in Column B is greater
The two quantities are equal
The relationship cannot be determined from the information given



The least common multiple of 6 and 10 is 30
The greatest common divisor of 80 and 140 is 20

So we have:
QUANTITY A: 30
QUANTITY B: 20

Answer: A
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The least common multiple of 6 and 10 [#permalink] New post   27 Oct 2022, 10:31
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Quantity A: The least common multiple of 6 and 10

6 = 2*3 = \(2^1 * 3^1\)
10 = 2*5 = \(2^1 * 5^1\)

To find the LCM take all the terms and take their highest power in all of the above.

=> LCM(6,10) = \(2^1 * 3^1 * 5^1\) = 30

Quantity B: The greatest common divisor of 80 and 140

80 = 16*5 = \(2^4 * 5^1\)
140 = 4 * 5 * 7 = \(2^2 * 5^1 * 7^1\)

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

=> GCD(80,140) = \(2^2 * 5^1\) = 20

Clearly, Quantity A(30) > Quantity B(20)

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 6 and 10 [#permalink]
27 Oct 2022, 10:31
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