Least Common Multiple (LCM) of 129 and 140
The least common multiple (LCM) of 129 and 140 is 18060.
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 140?
First, calculate the GCD of 129 and 140 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 140 = 0 remainder 129 |
| 2 | 140 ÷ 129 = 1 remainder 11 |
| 3 | 129 ÷ 11 = 11 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 32 | 160 |
| 191 and 96 | 18336 |
| 123 and 117 | 4797 |
| 189 and 39 | 2457 |
| 56 and 81 | 4536 |