If 1 is the greatest common factor of two numbers, what can you say about their least common multiple

Question

Im dealing with great common factor and least common multiples 

Answer 1

If their greatest common factor is 1, then one of the two numbers must be a prime number.  Their least common multiple must be the product of the two numbers.

 

For example:

 

5 and 7 are prime numbers because their only factors are 1 and themselves.  If you multiply these numbers, you get the product of 35, which is their least common multiple.

 

Another example:

 

5 and 9, in which 5 is the only prime number here.  The least multiple these numbers have in common is 45.

Answer 2

 

If the GCD(a,b) = 1  then the two numbers are said to be relatively prime.  They don't need to be prime numbers in themselves, it just means they have no common factors other than 1 and they are "prime with respect to each other."

 

It is true that if GCD(a,b) = 1 then LCM(a,b) = a*b.   

 

Example:

   8  = 2*2*2

   15 = 3*5

 

GCD(8,15) = 1  so  LCM(8,15) = 8*15 = 120

 

[ In fact the general case is  LCM(a,b) = a*b / GCD(a,b) ]