Least Common Multiple (LCM) of 129 and 142
The least common multiple (LCM) of 129 and 142 is 18318.
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 142?
First, calculate the GCD of 129 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 142 = 0 remainder 129 |
| 2 | 142 ÷ 129 = 1 remainder 13 |
| 3 | 129 ÷ 13 = 9 remainder 12 |
| 4 | 13 ÷ 12 = 1 remainder 1 |
| 5 | 12 ÷ 1 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 78 and 19 | 1482 |
| 51 and 57 | 969 |
| 89 and 17 | 1513 |
| 93 and 193 | 17949 |
| 49 and 135 | 6615 |