SOLUTION: The greatest common factor of 72 and X is 3. The least common multiple of 72 and X is 1800. What must be true? a) X is less than 72 b) X is multiple of 5. c) X is a multiple o

Algebra ->  Algebra  -> Divisibility and Prime Numbers -> SOLUTION: The greatest common factor of 72 and X is 3. The least common multiple of 72 and X is 1800. What must be true? a) X is less than 72 b) X is multiple of 5. c) X is a multiple o      Log On

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Question 234957: The greatest common factor of 72 and X is 3. The least common multiple of 72 and X is 1800. What must be true?
a) X is less than 72
b) X is multiple of 5.
c) X is a multiple of 72.
d) X is a factor of 3.
e) X is even

Answer by jsmallt9(606) About Me  (Show Source):
You can put this solution on YOUR website!
Probably the easiest way to solve this is to understand the relationship that exists between the LCM and GCF of two numbers. (Important: This only applies to two numbers, not 3, 4, etc.)
If our two numbers are a and b:
LCM = (a*b)/GCF

Putting the numbers (and x) from your problem we get:

which simplifies to:

Solving this (by dividing both sides by 24):

From this we can see that (a), (c), (d) and (e) are not true. Only (b) is true.