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PS - Easy One

by f2001290 » Fri Jun 15, 2007 6:40 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. 2,100
E. 4,900

Either the OA is wrong or I am bad at calculations. OA after few explanations
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by jayhawk2001 » Fri Jun 15, 2007 7:10 am
Is it A - 600 ?
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by f2001290 » Fri Jun 15, 2007 8:59 am
Calculation Mistake - OA is A
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by jayhawk2001 » Fri Jun 15, 2007 9:02 am
Some rationale behind my answer A.

If this is wrong, can some kind soul please tell me where I have gone
wrong.

90 = 9 * 10
196 = 49 * 4
300 = 3 * 100

LCM, as I understand, should prune the common factors
i.e. LCM = product of 3 / (duplicate common factors)

Going by the above, LCM = 9 * 49 * 100 (i.e. remaining factors 10, 4
and 3 are already included in the product)

700, 900, 2100 and 4900 are all factors of above LCM. Only 600 sticks out.
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by f2001290 » Fri Jun 15, 2007 9:08 am
Jay - your approach is perfect. I made a mistake in calculating LCM.
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by Brent@GMATPrepNow » Thu Oct 17, 2019 8:22 am
f2001290 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. 2,100
E. 4,900
90 = (2)(3)(3)(5)
196 = (2)(2)(7)(7)
300 = (2)(2)(3)(5)(5)

The least common multiple of 90, 196, and 300 = (2)(2)(3)(3)(5)(5)(7)(7)
So, M = (2)(2)(3)(3)(5)(5)(7)(7)

Now check the answer choices...
A) 600
600 = (2)(2)(2)(3)(5)(5)
For 600 to be a factor of M, there must be three 2's, one 3 and two 5's "hiding" in the prime factorization of M. Since, M only has two 2's in its prime factorization, 600 is NOT a factor of M.

Answer: A

ASIDE: I thought it might be useful to show one way to find the LCM of large numbers:
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Brent Hanneson - Creator of GMATPrepNow.com
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