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nervesofsteel
- Legendary Member
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- Joined: Thu Aug 14, 2008 11:51 pm
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To find the LCM of three numbers, use the prime factorization:
90 = 9*10 = 2*(3^2)*5
196 = 200 - 5 = 49*4 = (2^2)(7^2)
300 = 3*100 = (2^2)*3*(5^2)
You're supposed to use the highest powers of every prime factor, so LCM will be (2^2)*(3^2)*(5^2)*(7^2).
Now, given the OA, I'm tempted to say that the question is actually asking for the number that IS NOT a factor of the LCM of the 3 numbers. In this case, 600 would indeed be it, since 600 = 6*100 = 2*3*(2^2)*(5^2) = (2^3)*3*(5^2). As you can see, the fact that 2 is in the third power is actually the issue here, since we don't have a 2 to the third power in the LCM.
The prime factorization of the rest of your options proves that they are all factors if the LCM:
B. 700 = (2^2)*(5^2)*7
C. 900 = (2^2)*(3^2)*(5^2)
D. 2100 = (2^2)*3*(5^2)*7
E. 4900 = (2^2)*(5^2)*(7^2).
The trick is to notice that the powers of all the prime factors of say 700 are less than those of the LCM.
