If the LCM(x, 25) is 100, what is the value of x?

Question

If the LCM(x, 25) is 100, what is the value of x?
1. GCD(x, 5) is 1.
2. LCM(x, 8) is 8.

GMATinsight · Answer

LCM (x, 25) = 100

i.e. x can be {4, 20, 100}

Question; x = ?

Statement 1 : GCD(x, 5) is 1

i.e. x is NOT a multiple of 5 
i.e .x can only be 4 out of possible choices {4, 20, 100}

SUFFICIENT

Statement 2 : LCM(x, 8) is 8

i.e. x can be {1, 2, 4, 8}

But we also know that x can be only one of {4, 20, 100}

ie.. x = 4

SUFFICIENT

Answer: Option D

tittoo · Answer

Is there a way to solve this through prime factorization method?
Can someone show how to do that?

KunFu · Answer

100 = 5^2 * 2^2

LCM (x,25) = 100

25 = 5^2

Therefore, x must have  2^2  and can have either  5^2  or  5  or no powers of  5

Case 1: x = 2^2 * 5^0 = 4

Case 2: x = 2^2 * 5 = 20

Case 3: x = 2^2 * 5^2 = 100

Hence 3 possible values, then proceed according to Statements
St 1: Gives 4 as a possibility
St 2: Gives 4 as a possibility

Hence D

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