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
5-Day Free Trial
5-day free, full-access trial TTP
Available with Beat the GMAT members only code
MORE DETAILS
Least common multiple question
This topic has expert replies
GMAT/MBA Expert
-
Brent@GMATPrepNow
- GMAT Instructor
- Posts: 16207
- Joined: Mon Dec 08, 2008 6:26 pm
- Location: Vancouver, BC
- Thanked: 5254 times
- Followed by:1268 members
- GMAT Score:770
I thought it might be useful to show one way to find the LCM of large numbers: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
Brent Hanneson - Creator of GMATPrepNow.com
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.
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.
