Least Common Multiple (LCM) of 129 and 199
The least common multiple (LCM) of 129 and 199 is 25671.
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 199?
First, calculate the GCD of 129 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 199 = 0 remainder 129 |
| 2 | 199 ÷ 129 = 1 remainder 70 |
| 3 | 129 ÷ 70 = 1 remainder 59 |
| 4 | 70 ÷ 59 = 1 remainder 11 |
| 5 | 59 ÷ 11 = 5 remainder 4 |
| 6 | 11 ÷ 4 = 2 remainder 3 |
| 7 | 4 ÷ 3 = 1 remainder 1 |
| 8 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 26 | 4342 |
| 99 and 168 | 5544 |
| 165 and 82 | 13530 |
| 128 and 113 | 14464 |
| 73 and 45 | 3285 |