Least Common Multiple (LCM) of 129 and 180
The least common multiple (LCM) of 129 and 180 is 7740.
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 180?
First, calculate the GCD of 129 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 180 = 0 remainder 129 |
| 2 | 180 ÷ 129 = 1 remainder 51 |
| 3 | 129 ÷ 51 = 2 remainder 27 |
| 4 | 51 ÷ 27 = 1 remainder 24 |
| 5 | 27 ÷ 24 = 1 remainder 3 |
| 6 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 126 | 756 |
| 29 and 16 | 464 |
| 136 and 92 | 3128 |
| 49 and 112 | 784 |
| 156 and 137 | 21372 |