Least Common Multiple (LCM) of 129 and 184
The least common multiple (LCM) of 129 and 184 is 23736.
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 184?
First, calculate the GCD of 129 and 184 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 184 = 0 remainder 129 |
| 2 | 184 ÷ 129 = 1 remainder 55 |
| 3 | 129 ÷ 55 = 2 remainder 19 |
| 4 | 55 ÷ 19 = 2 remainder 17 |
| 5 | 19 ÷ 17 = 1 remainder 2 |
| 6 | 17 ÷ 2 = 8 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 35 | 2415 |
| 75 and 180 | 900 |
| 120 and 110 | 1320 |
| 58 and 76 | 2204 |
| 37 and 31 | 1147 |