Least Common Multiple (LCM) of 129 and 107
The least common multiple (LCM) of 129 and 107 is 13803.
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 107?
First, calculate the GCD of 129 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 107 = 1 remainder 22 |
| 2 | 107 ÷ 22 = 4 remainder 19 |
| 3 | 22 ÷ 19 = 1 remainder 3 |
| 4 | 19 ÷ 3 = 6 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 79 and 169 | 13351 |
| 100 and 159 | 15900 |
| 107 and 198 | 21186 |
| 27 and 75 | 675 |
| 144 and 47 | 6768 |