Least Common Multiple (LCM) of 129 and 190
The least common multiple (LCM) of 129 and 190 is 24510.
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 129 and 190?
First, calculate the GCD of 129 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 190 = 0 remainder 129 |
| 2 | 190 ÷ 129 = 1 remainder 61 |
| 3 | 129 ÷ 61 = 2 remainder 7 |
| 4 | 61 ÷ 7 = 8 remainder 5 |
| 5 | 7 ÷ 5 = 1 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 55 | 3795 |
| 110 and 31 | 3410 |
| 180 and 110 | 1980 |
| 45 and 161 | 7245 |
| 44 and 22 | 44 |