LCM

To find the LCM of three numbers, use the prime factorization:
90 = 9*10 = 2*(3^2)*5
196 = 200 - 5 = 49*4 = (2^2)(7^2)
300 = 3*100 = (2^2)*3*(5^2)

You're supposed to use the highest powers of every prime factor, so LCM will be (2^2)*(3^2)*(5^2)*(7^2).

Now, given the OA, I'm tempted to say that the question is actually asking for the number that IS NOT a factor of the LCM of the 3 numbers. In this case, 600 would indeed be it, since 600 = 6*100 = 2*3*(2^2)*(5^2) = (2^3)*3*(5^2). As you can see, the fact that 2 is in the third power is actually the issue here, since we don't have a 2 to the third power in the LCM.

The prime factorization of the rest of your options proves that they are all factors if the LCM:
B. 700 = (2^2)*(5^2)*7
C. 900 = (2^2)*(3^2)*(5^2)
D. 2100 = (2^2)*3*(5^2)*7
E. 4900 = (2^2)*(5^2)*(7^2).

The trick is to notice that the powers of all the prime factors of say 700 are less than those of the LCM.

nervesofsteel wrote:M is the least common multiple of 90,196 and 300. Which of the following is the factor of M

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

OAA

You are correct , i took a wrong LCM .... and yes the question reads NOT a factor of M..

apologies for the typo....