Least Common Multiple (LCM) of 129 and 182
The least common multiple (LCM) of 129 and 182 is 23478.
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 182?
First, calculate the GCD of 129 and 182 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 182 = 0 remainder 129 |
| 2 | 182 ÷ 129 = 1 remainder 53 |
| 3 | 129 ÷ 53 = 2 remainder 23 |
| 4 | 53 ÷ 23 = 2 remainder 7 |
| 5 | 23 ÷ 7 = 3 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 121 | 13915 |
| 22 and 44 | 44 |
| 197 and 35 | 6895 |
| 105 and 28 | 420 |
| 165 and 12 | 660 |