Least Common Multiple (LCM) of 80 and 189
The least common multiple (LCM) of 80 and 189 is 15120.
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 80 and 189?
First, calculate the GCD of 80 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 189 = 0 remainder 80 |
| 2 | 189 ÷ 80 = 2 remainder 29 |
| 3 | 80 ÷ 29 = 2 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 180 | 1980 |
| 129 and 43 | 129 |
| 107 and 139 | 14873 |
| 156 and 106 | 8268 |
| 188 and 168 | 7896 |