Least Common Multiple (LCM) of 180 and 129
The least common multiple (LCM) of 180 and 129 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 180 and 129?
First, calculate the GCD of 180 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 129 = 1 remainder 51 |
| 2 | 129 ÷ 51 = 2 remainder 27 |
| 3 | 51 ÷ 27 = 1 remainder 24 |
| 4 | 27 ÷ 24 = 1 remainder 3 |
| 5 | 24 ÷ 3 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 35 | 4935 |
| 185 and 111 | 555 |
| 134 and 92 | 6164 |
| 130 and 30 | 390 |
| 197 and 101 | 19897 |