X is the least common multiple of 96, 196, 300, which number below is

In case some students are wondering how we find the LCM of 96. 196 and 300, here's a step-by-step solution:

If X is a multiple of 96, then X = 96k (where k is some positive integer)
In other words, X = (2)(2)(2)(2)(2)(3)(k)

196 = (2)(2)(7)(7)
Since X is a multiple of 196, X needs two 2's and two 7's in its prime factorization.
We already know that X = (2)(2)(2)(2)(2)(3)(k), so we already have the two 2's. BUT, we need to add two 7's to the product.
We get: X = (2)(2)(2)(2)(2)(3)(7)(7)(k)

300 = (2)(2)(3)(5)(5)
Since X is a multiple of 300, then X needs two 2's, one 3 and two 5's in its prime factorization.
We already know that X = (2)(2)(2)(2)(2)(3)(7)(7)(k), so we already have the two 2's, and the one 3. BUT, we need to add two 5's to the product.
We get: X = (2)(2)(2)(2)(2)(3)(5)(5)(7)(7)(k)

So, the very smallest value of X = (2)(2)(2)(2)(2)(3)(5)(5)(7)(7)

Now scan the answer choices....

When we get to C (900), we can see that X must be divisible by 9 (Since 9 is a factor of 900)
For X to be divisible by 9, X must have two 3's in its prime factorization.
However, we do NOT have two 3's in (2)(2)(2)(2)(2)(3)(5)(5)(7)(7)

Answer: C

Cheers,
Brent

96 = 2^5 * 3
196 = 2^2 * 7^2
300 = 2^2 * 3 * 5^2

LCM(96,196,300) = X = 2^5*3*5^2*7^2

From the options, we can see that C = 900 which has 3^2 but maximum power of 3 in X is 1. so 900 cannot be a factor of X.
IMO - C

Breaking each number into prime factors, we have:

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

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

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

So the LCM is 2^5 x 3^1 x 5^2 x 7^2.

Since 900 = 2^2 x 3^2 x 5^2, it can’t be a factor of X because it has more factors of 3 than X does.

Answer: C

\(f(96):2^53\)
\(f(196):2^27^2\)
\(f(300):2^2*5^23\)
\(lcm(96,196,300):3*2^55^27^2\)

Ans (C): 9 is not factor of X

All choices have a factor of 100, so we only concern with the factor other than 100:
A. 6=2*3
B. 7
C. 9=3*3
D. 21=3*7
E. 49=7*7

Check whether combination of 96, 196, 300 has sufficient 3*3 and 7*7 (and a single 2 beside 100):
96= 2^5*3, 196= 2*2*7*7, and 300= 3*100.

Obviously, choice (C) is the answer since it has more factor of 3 than it should have been.

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Breaking each number into prime factors, we have:

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

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

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

Thus, the LCM is 2^5 x 3^1 x 5^2 x 7^2

Since 900 has two 3s, 900 cannot be a factor of X.

Answer: C

Asked: X is the least common multiple of 96, 196, 300, which number below is not factor of X?

96 = 2^5*3
196 = 7^2*2^2
300 = 2^2*5^2*3

LCM (96,196,300) = 2^5*3*5^2*7^2

A. 600 = 2^3*5^2*3; Factor of 2^5*3*5^2*7^2
B. 700 = 7*2^2*5^2; Factor of 2^5*3*5^2*7^2
C. 900 = 2^2*3^2*5^2; Not a factor of 2^5*3*5^2*7^2
D. 2100; = 2^2*3*5^2*7; Factor of 2^5*3*5^2*7^2
E. 4900 = 2^2*5^2*7^2; Factor of 2^5*3*5^2*7^2

IMO C

least common multiple of 96, 196, 300 = x= 2^5 *3*5^2*7^2

So, C.

it's quite simple just we get every other prime number till 7 squared without 3 hence imo C

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