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LCM - set11 q36

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arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Mon Oct 08, 2007 12:34 am

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

Should have been straightforward, but my answer isn't the same as OA. Pls explain. Thanks.

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Source: Beat The GMAT — Problem Solving | Mon Oct 08, 2007 12:34 am

samirpandeyit62: Master | Next Rank: 500 Posts; Posts: 460; Joined: Sun Mar 25, 2007 7:42 am; Thanked: 27 times

by samirpandeyit62 » Mon Oct 08, 2007 6:18 am

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

to find the LCM we can exploit the two largest nos i.e 196 & 300 coz these will be the ones with lesser common multiples.

so we have only a multiple of 196 which gives 2 trailing zero's will be divisible by 300 i.e 3 *100

so min nos which will give 2 trailing zero's is 25

4900/300 gives a remainder of 1 so three times of this should be divisible by 300 & 9 times shoul be divisible by 90

i.e 4900*9 =44100 is the LCM

now only 600 does not divide 4900 * 9 so A must be the ans

Regards
Samir

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ajith: Legendary Member; Posts: 1275; Joined: Thu Sep 21, 2006 11:13 pmFollowed by: 2 members; Location: Arabian Sea; Thanked: 125 times

Re: LCM - set11 q36

by ajith » Mon Oct 08, 2007 7:00 am

arocks 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

Should have been straightforward, but my answer isn't the same as OA. Pls explain. Thanks.

90 = 2*3^2*5
196 = 2^6*3
300 = 2^2*3*5
LCM = 2^6*3^2*5^2

Clearly 700,2100 and 4900 are not the factors of this
Check whether the number given in the question is 198 instead of 196

Always borrow money from a pessimist, he doesn't expect to be paid back.

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ldoolitt: Master | Next Rank: 500 Posts; Posts: 184; Joined: Sat Apr 14, 2007 9:23 am; Location: Madison, WI; Thanked: 17 times

Re: LCM - set11 q36

by ldoolitt » Mon Oct 08, 2007 7:13 am

ajith wrote:
90 = 2*3^2*5
196 = 2^6*3
300 = 2^2*3*5
LCM = 2^6*3^2*5^2

Clearly 700,2100 and 4900 are not the factors of this
Check whether the number given in the question is 198 instead of 196

I got different factors

90 => 2 * 3^2 * 5
196 => 2^2 * 7^2
300 => 2^2 * 3 * 5^2

which gives you

lcm => 2^2 * 3^2 * 5^2 * 7^2 = 44100

only (a) does not evenly divide into 44100 as first replier said.

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arocks: Master | Next Rank: 500 Posts; Posts: 127; Joined: Tue Oct 02, 2007 9:35 am; Thanked: 1 times

by arocks » Mon Oct 08, 2007 11:11 am

Thanks guys....i slipped up while calculating the lcm.

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