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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # X is the least common multiple of 96, 196, 300, which number below is

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Math Expert V
Joined: 02 Sep 2009
Posts: 61436
X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 66% (02:17) correct 34% (02:28) wrong based on 154 sessions

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X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

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VP  V
Joined: 20 Jul 2017
Posts: 1330
Location: India
Concentration: Entrepreneurship, Marketing
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Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

96 = 2^5*3
196 = 2^2*7^2
300 = 2^2*3*5^2

X = LCM(96, 196, 300) = 2^5*3*5^2*7^2

Since 900 = 2^2*3^2*5^2 and X has only 3^1 as a factor, 900 cannot be the factor of X

IMO Option C

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GMAT Club Legend  V
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Posts: 5906
Location: India
Concentration: Sustainability, Marketing
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Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

LCM of 96, 196, 300 = 2^5*7^2*3*5^2
out of given options C ; 900 is not factor of 2^5*7^2*3*5^2
IMO C
GMAT Club Legend  V
Joined: 11 Sep 2015
Posts: 4345
Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Top Contributor
Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

In case some students are wondering how we find the LCM of 96. 196 and 300, here's a step-by-step solution:

If X is a multiple of 96, then X = 96k (where k is some positive integer)
In other words, X = (2)(2)(2)(2)(2)(3)(k)

196 = (2)(2)(7)(7)
Since X is a multiple of 196, X needs two 2's and two 7's in its prime factorization.
We already know that X = (2)(2)(2)(2)(2)(3)(k), so we already have the two 2's. BUT, we need to add two 7's to the product.
We get: X = (2)(2)(2)(2)(2)(3)(7)(7)(k)

300 = (2)(2)(3)(5)(5)
Since X is a multiple of 300, then X needs two 2's, one 3 and two 5's in its prime factorization.
We already know that X = (2)(2)(2)(2)(2)(3)(7)(7)(k), so we already have the two 2's, and the one 3. BUT, we need to add two 5's to the product.
We get: X = (2)(2)(2)(2)(2)(3)(5)(5)(7)(7)(k)

So, the very smallest value of X = (2)(2)(2)(2)(2)(3)(5)(5)(7)(7)

When we get to C (900), we can see that X must be divisible by 9 (Since 9 is a factor of 900)
For X to be divisible by 9, X must have two 3's in its prime factorization.
However, we do NOT have two 3's in (2)(2)(2)(2)(2)(3)(5)(5)(7)(7)

Cheers,
Brent
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Joined: 20 Aug 2017
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Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

96 = 2^5 * 3
196 = 2^2 * 7^2
300 = 2^2 * 3 * 5^2

LCM(96,196,300) = X = 2^5*3*5^2*7^2

From the options, we can see that C = 900 which has 3^2 but maximum power of 3 in X is 1. so 900 cannot be a factor of X.
IMO - C
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Posts: 9461
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Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Breaking each number into prime factors, we have:

96 = 32 x 3 = 2^5 x 3^1

196 = 4 x 49 = 2^2 x 7^2

300 = 3 x 100 = 2^2 x 3^1 x 5^2

So the LCM is 2^5 x 3^1 x 5^2 x 7^2.

Since 900 = 2^2 x 3^2 x 5^2, it can’t be a factor of X because it has more factors of 3 than X does.

_________________

# Scott Woodbury-Stewart

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Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

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VP  P
Joined: 24 Nov 2016
Posts: 1224
Location: United States
Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

$$f(96):2^53$$
$$f(196):2^27^2$$
$$f(300):2^2*5^23$$
$$lcm(96,196,300):3*2^55^27^2$$

Ans (C): 9 is not factor of X
Director  V
Joined: 30 Sep 2017
Posts: 674
GMAT 1: 720 Q49 V40 GPA: 3.8
X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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All choices have a factor of 100, so we only concern with the factor other than 100:
A. 6=2*3
B. 7
C. 9=3*3
D. 21=3*7
E. 49=7*7

Check whether combination of 96, 196, 300 has sufficient 3*3 and 7*7 (and a single 2 beside 100):
96= 2^5*3, 196= 2*2*7*7, and 300= 3*100.

Obviously, choice (C) is the answer since it has more factor of 3 than it should have been.

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Target Test Prep Representative V
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 9461
Location: United States (CA)
Re: X is the least common multiple of 96, 196, 300, which number below is  [#permalink]

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Bunuel wrote:
X is the least common multiple of 96, 196, 300, which number below is not factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Are You Up For the Challenge: 700 Level Questions: 700 Level Questions

Breaking each number into prime factors, we have:

96 = 3 x 32 = 2^5 x 3^1

196 = 4 x 49 = 2^2 x 7^2

300 = 3 x 100 = 2^2 x 3^1 x 5^2

Thus, the LCM is 2^5 x 3^1 x 5^2 x 7^2

Since 900 has two 3s, 900 cannot be a factor of X.

_________________

# Scott Woodbury-Stewart

Founder and CEO

Scott@TargetTestPrep.com

See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews

If you find one of my posts helpful, please take a moment to click on the "Kudos" button. Re: X is the least common multiple of 96, 196, 300, which number below is   [#permalink] 21 Jan 2020, 08:34
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