Basic Mathematics Solved Problems | Topics - Contents
Greatest Common Factor and Least Common Multiple
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.
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
- Find the GCF of 45 and 60
| 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 | |
| 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 | |