f2001290 wrote:If M is the least common multiple of 90, 196, and 300, which of the following is NOT a factor of M?
A. 600
B. 700
C. 900
D. 2,100
E. 4,900

90 = (2)(3)(3)(5)
196 = (2)(2)(7)(7)
300 = (2)(2)(3)(5)(5)

The least common multiple of 90, 196, and 300 = (2)(2)(3)(3)(5)(5)(7)(7)
So, M = (2)(2)(3)(3)(5)(5)(7)(7)

Now check the answer choices...
A) 600
600 = (2)(2)(2)(3)(5)(5)
For 600 to be a factor of M, there must be three 2's, one 3 and two 5's "hiding" in the prime factorization of M. Since, M only has two 2's in its prime factorization, 600 is NOT a factor of M.

Answer: A

ASIDE: I thought it might be useful to show one way to find the LCM of large numbers: