Greatest Common Factor (GCF) and

For example, find the GCF of 12 and 8: Factors of 12 : 1 , 2 , 3 , 4 , 6 , 12 Factors of 8 : 1 , 2 , 4 , 8 The highest number that appears in both lists is 4, so 4 is the GCF of 12 and 8. Now, can you find the GCF of 22 and 33? Factors of 22: _________ Factors of 33: _________ GCF(22,33) = _____ 
For example, find the LCM of 6 and 8: Multiples of 6: 12 18 24 30 36 42 48 ... Multiples of 8: 16 24 32 40 48 56 64 ... The first number that appears in both lists is 24. (48 appears also, but it is not 'least'), so 24 is the LCM of 6 and 8. Now, can you find the LCM of 10 and 35? Multiples of 10: ________________ Multiples of 35: ________________ LCM(10,35) = _____ 
a x b = LCM(a,b) x GCF(a,b) Simply put, this says that the greatest common factor of a and b, when multiplied by the least common multiple of a and b, is the product of a and b where a and b are positive integers.  
Finding the GCF when you know the LCM GCF(a,b) = (a x b) / LCM(a,b) For our LCM example of 6 and 8 we have: GCF (6 , 8) = 6 x 8 / LCM (12 , 8) Since the LCM of 6 and 8 is 24, we have: GCF (6 , 8) = 6 x 8 / 24 = 48/24 = 2 
Finding the LCM when you know the GCF LCM(a,b) = (a x b) / GCF(a,b) For our GCF example of 12 and 8 we have: LCM (12 , 8) = 12 x 8 / GCF (12 , 8) Since the GCF of 12 and 8 is 4, we have: LCM (12 , 8) = 12 x 8 / 4 = 12 x 2 = 24 
Finding b when you know a, the GCF of a and b and their LCM: b = GCF(a,b) x LCM(a,b) / a Example: What is b when a = 8, the GCF(a,b) = 4 and their LCM is 24? b = 4 x 24 / 8 = 12 

Now here's a problem for you: The GCF of a and b is 12 and their LCM is 240. a is 48. What is b? b = GCF x LCM / 48 = ___ x ___ / 48 b = _____ 