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Least common multiple question

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by jfranco23 » Mon Mar 09, 2009 4:05 pm
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. 2100
E. 4900
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by devesh99 » Mon Mar 09, 2009 6:20 pm
LCM is 44100

2*2*3*3*5*5*7*7 = 44100

Ans (A)
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Re: Least common multiple question

by Brent@GMATPrepNow » Mon Mar 09, 2009 8:06 pm
jfranco23 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. 2100
E. 4900
I thought it might be useful to show one way to find the LCM of large numbers:
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by mrsmarthi » Mon Mar 09, 2009 8:23 pm
IMO E.

Express each number in prime factors with each prime factor in exponetation notation.

LCM is the product of distinct prime factors having the highest exponents.

90 = 2 * 3^2 * 5
196 = 2^2 * 7^2
300 = 2^3 * 3 * 5^2
-------------------------
LCM = 2^3 * 3^2 * 5^2 * 7^2

Now coming to the ans choices all of them are multiples are 100 = 2^2 * 5^2.

Cancelling this part from the LCM we have 2 * 3^2 * 7^2.

Only E(49) cannot be formed from the above left over of LCM.
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by cramya » Mon Mar 09, 2009 9:00 pm
Mrs.Marthi,
I think u may have accidentally included an extra 2 in the lcm which led you to E.

Regards,
Cramya
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