Greatest Common Factor(GCF) is the largest number that can divide set or pair of numbers with out a remainder.
Example: The GCF of 4 and 10 is 2, because 2 can both divide 4 and 10 with out a remainder.
Least Common Multiple(LCM) is the smallest number divisible by a set or pair of numbers.
Example: The LCM of 4 and 10 is 40, because 40 is divisible by both 10 and 4.
Sample Calculations:
- Find the GCF and LCM of 80, 120, 160
Number |
Prime Factors |
80 |
2 x 2 x 2 x 2 x 5 |
120 |
2 x 2 x 2 x 3 x 5 |
160 |
2 x 2 x 2 x 2 x 2 x 5 |
Similar factors: 5 x 2 x 2 x 2 = 40. Thus the GCF is 40 |
Factors: 5 x 2 x 2 x 2 x 2 x 2 x 3= 480. Thus the LCM is 480 |
- Find the GCF of 45 and 60
Number |
Prime Factors |
45 |
5 x 3 x 3 |
60 |
5 x 3 x 2 x 2 |
Similar factors: 5 x 3 = 15. Thus the GCF is 15 |
Factors: 5 x 3 x 3 x 2 x 2 = 180. Thus the LCM is 180 |