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X is the least common multiple of 96, 196, 300, which number below is
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01 Nov 2019, 04:30
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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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Re: X is the least common multiple of 96, 196, 300, which number below is
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01 Nov 2019, 05:07
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 Questions96 = 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 Posted from my mobile device



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Re: X is the least common multiple of 96, 196, 300, which number below is
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01 Nov 2019, 06:13
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 QuestionsLCM 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



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Re: X is the least common multiple of 96, 196, 300, which number below is
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01 Nov 2019, 06:50
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 QuestionsIn case some students are wondering how we find the LCM of 96. 196 and 300, here's a stepbystep 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) Now scan the answer choices.... 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) Answer: C Cheers, Brent
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Re: X is the least common multiple of 96, 196, 300, which number below is
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19 Nov 2019, 00:42
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 Questions96 = 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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Re: X is the least common multiple of 96, 196, 300, which number below is
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22 Nov 2019, 12:11
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 QuestionsBreaking 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. Answer: C
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Re: X is the least common multiple of 96, 196, 300, which number below is
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24 Nov 2019, 07:05
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



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X is the least common multiple of 96, 196, 300, which number below is
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15 Jan 2020, 09:35
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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Re: X is the least common multiple of 96, 196, 300, which number below is
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21 Jan 2020, 08:34
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 QuestionsBreaking 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. Answer: C
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Re: X is the least common multiple of 96, 196, 300, which number below is
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21 Jan 2020, 08:34






