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# If the least common multiple of integers x and y is 840, what is the

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Math Expert
Joined: 02 Sep 2009
Posts: 51072
If the least common multiple of integers x and y is 840, what is the  [#permalink]

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22 Dec 2016, 01:33
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Difficulty:

45% (medium)

Question Stats:

65% (01:20) correct 35% (01:50) wrong based on 73 sessions

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If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 28.
(2) y = 168

_________________
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
Re: If the least common multiple of integers x and y is 840, what is the  [#permalink]

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22 Dec 2016, 03:37
1
(1) The greatest common factor of x and y is 28

x=28a, y=28b where a, b are co-prime integers.

LCM (x,y) = 28ab

ab = 30

ab = 2*15, 3*10 ... Not sufficient.

(2) y = 168 Clearly not sufficient

(1) & (2) taken together

LCM (x,y)*GCF(x,y) = xy

Sufficient

C
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Joined: 04 Mar 2016
Posts: 45
Location: India
Re: If the least common multiple of integers x and y is 840, what is the  [#permalink]

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22 Dec 2016, 10:14
vitaliyGMAT wrote:
(1) The greatest common factor of x and y is 28

x=28a, y=28b where a, b are co-prime integers.

LCM (x,y) = 28ab

ab = 30

ab = 2*15, 3*10 ... Not sufficient.

(2) y = 168 Clearly not sufficient

(1) & (2) taken together

LCM (x,y)*GCF(x,y) = xy

Sufficient

C

Please elaborate the reply with Examples of you can. Or with detailed working

Omkar Kamat
When The Going Gets Tough, The Tough Gets Going !!
Senior Manager
Joined: 13 Oct 2016
Posts: 367
GPA: 3.98
If the least common multiple of integers x and y is 840, what is the  [#permalink]

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22 Dec 2016, 11:23
1
Dear Omkar Kamat

Sorry for late reply, quite a busy day.

(1) The greatest common factor of x and y is 28

We have LCM 840 and GCF 28

Our numbers can be 28 and 840, 56 and 140, 84 and 280 etc. Our numbers are in the form 28a and 28b, but a and b can take different values wich satisfy both LCM 840 and GCF 28. Not sufficient.

(2) y = 168

y=2^3*3*7 When we calculate LCM we take max powers of prime numbers (you can also look at this as a union of two sets). We can make an inference, that x must have one factor of 5, but it may have or may not have 3, 7 or 2.

840 = 2^3*3*5*7 -----> x=5 or x=3*5 or x=2*3*5 ... or x = 2^3*3*5*7

Not sufficient.

(1) & (2) together.

We have very important relationship:

LCM (x,y)*GCF(x,y) = x*y

Plugging in our values we can get our x. Sufficient.

Hope it helps

Best regards
Intern
Joined: 17 Jul 2016
Posts: 24
Re: If the least common multiple of integers x and y is 840, what is the  [#permalink]

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25 Dec 2016, 10:58
1
Bunuel wrote:
If the least common multiple of integers x and y is 840, what is the value of x?

(1) The greatest common factor of x and y is 28.
(2) y = 168

C
If x and y are two positive integers, LCM * GCF = x* y
Stmnt 1: Just the GCF will give you the product of the two numbers. Not their individual values.
Stmnt 2: Knowing the value of y and LCM is not sufficient to get x.

Using both together, we can get the value of x
Non-Human User
Joined: 09 Sep 2013
Posts: 9101
Re: If the least common multiple of integers x and y is 840, what is the  [#permalink]

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03 Jul 2018, 21:26
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Re: If the least common multiple of integers x and y is 840, what is the &nbs [#permalink] 03 Jul 2018, 21:26
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