Least Common Multiple (LCM) of 108 and 80
The least common multiple (LCM) of 108 and 80 is 2160.
What is the Least Common Multiple (LCM)?
The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.
Formula for LCM
The LCM of two numbers can be calculated using their GCD:
LCM(a, b) = |a × b| ÷ GCD(a, b)
How to Calculate the LCM of 108 and 80?
First, calculate the GCD of 108 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 80 = 1 remainder 28 |
| 2 | 80 ÷ 28 = 2 remainder 24 |
| 3 | 28 ÷ 24 = 1 remainder 4 |
| 4 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 158 | 16906 |
| 22 and 39 | 858 |
| 130 and 185 | 4810 |
| 198 and 97 | 19206 |
| 56 and 178 | 4984 |