Least Common Multiple (LCM) of 185 and 129
The least common multiple (LCM) of 185 and 129 is 23865.
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 185 and 129?
First, calculate the GCD of 185 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 185 ÷ 129 = 1 remainder 56 |
| 2 | 129 ÷ 56 = 2 remainder 17 |
| 3 | 56 ÷ 17 = 3 remainder 5 |
| 4 | 17 ÷ 5 = 3 remainder 2 |
| 5 | 5 ÷ 2 = 2 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 32 and 23 | 736 |
| 113 and 131 | 14803 |
| 188 and 66 | 6204 |
| 80 and 98 | 3920 |
| 84 and 18 | 252 |