Least common multiple question

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jfranco23: Senior | Next Rank: 100 Posts; Posts: 75; Joined: Fri Jan 16, 2009 2:00 pm; Thanked: 1 times; GMAT Score:550

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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Source: Beat The GMAT — Problem Solving | Mon Mar 09, 2009 4:05 pm

devesh99: Junior | Next Rank: 30 Posts; Posts: 14; Joined: Wed Feb 18, 2009 4:56 pm; Thanked: 1 times

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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Brent@GMATPrepNow: GMAT Instructor; Posts: 16207; Joined: Mon Dec 08, 2008 6:26 pmFollowed by: 1268 members; Location: Vancouver, BC; Thanked: 5254 times; GMAT Score:770

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:

Brent Hanneson - Creator of GMATPrepNow.com

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mrsmarthi: Senior | Next Rank: 100 Posts; Posts: 45; Joined: Sun Nov 30, 2008 8:41 pm; Thanked: 4 times

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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cramya: Legendary Member; Posts: 2467; Joined: Thu Aug 28, 2008 6:14 pmFollowed by: 11 members; Thanked: 331 times

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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