Problem Solving

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.

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

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

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.

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