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 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)
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