SOLUTION: If N is the least common multiple of 10 and 18, what is the greatest common factor of 132 and N? A. 2 B. 3 C. 6 D. 11 E. 12

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Question 243157: If N is the least common multiple of 10 and 18, what is the greatest common factor of 132 and N?
A. 2 B. 3 C. 6 D. 11 E. 12
Answer by vleith(2983) (Show Source):
You can put this solution on YOUR website!
Both LCM and GCF require that you find the prime factorization for the given numbers. I'll assume you know how to do prime factorization. So here is a URL that does that legwork for you.
We need to find the LCM for 10 and 18
Factorize 10 --> 2,5
Factorize 18 --> 2, 3, 3
To find the LCM, you need to find the prime factors from each 10 and 18 that occur MOST. There is one 2 in both, one 5 in one and two 3's in the other. So the LCM is
Now factorize 132 --> 2 2 3 11
To find the GCF, you need to find only those prime factros that occur in BOTH 90 and 132 -- but now, instead of finding the ones that occur the most, take the ones that occur the fewest times.
Both 90 and 132 have 2 as a factor. But only one 2 in 90
Both have three as a factor too. Again only one three in 132.
That's it