X is the least common multiple of 96,196,300 . . . .

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 am; Followed by:3 members

X is the least common multiple of 96,196,300 . . . .

by VJesus12 » Tue Jun 05, 2018 1:33 am

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X is the least common multiple of 96, 196 and 300. Which number below is not a factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

The OA is the option C.

How can I know the factors of X? Is there a fast way for solving this PS question? I'd appreciate any help.

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Source: Beat The GMAT — Problem Solving | Tue Jun 05, 2018 1:33 am

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Scott@TargetTestPrep: GMAT Instructor; Posts: 8086; Joined: Sat Apr 25, 2015 10:56 am; Location: Los Angeles, CA; Thanked: 43 times; Followed by:29 members

by Scott@TargetTestPrep » Wed Jun 06, 2018 4:01 pm

VJesus12 wrote:X is the least common multiple of 96, 196 and 300. Which number below is not a factor of X?

A. 600
B. 700
C. 900
D. 2100
E. 4900

Breaking each number into primes, we have:

96 = 32 x 3 = 2^5 x 3^1

196 = 4 x 49 = 2^2 x 7^2

300 = 3 x 100 = 3^1 x 2^2 x 5^2

The LCM is 2^5 x 3^1 x 5^2 x 7^2

Since 900 = 3^2 x 100, we see that 900 cannot be a factor of X.

Answer: C

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