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 |
|---|---|
| 162 and 13 | 2106 |
| 157 and 157 | 157 |
| 114 and 123 | 4674 |
| 131 and 61 | 7991 |
| 12 and 154 | 924 |