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
How do you solve this?
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- rajkoneru
- RonPurewal
- Students
- Posts: 19744
- Joined: Tue Aug 14, 2007 8:23 am
To find the least common multiple, first break the numbers down into prime factorizations:
90 = 2.3.3.5
196 = 2.2.7.7
300 = 2.2.3.5.5
The least common multiple has to contain enough of each prime number so that ALL of these numbers go into it. Therefore, the least common multiple has two 2's, two 3's, two 5's, and two 7's. (Notice that we don't have to calculate this number!)
For a number NOT to be a factor, it must exceed at least one of these #s of factors. The only listed number that does so is 600 (= 2.2.2.3.5.5), which contains three 3's. Answer = A
90 = 2.3.3.5
196 = 2.2.7.7
300 = 2.2.3.5.5
The least common multiple has to contain enough of each prime number so that ALL of these numbers go into it. Therefore, the least common multiple has two 2's, two 3's, two 5's, and two 7's. (Notice that we don't have to calculate this number!)
For a number NOT to be a factor, it must exceed at least one of these #s of factors. The only listed number that does so is 600 (= 2.2.2.3.5.5), which contains three 3's. Answer = A
3 posts Page 1 of 1