Least Common Multiple (LCM) of 129 and 106
The least common multiple (LCM) of 129 and 106 is 13674.
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 106?
First, calculate the GCD of 129 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 106 = 1 remainder 23 |
| 2 | 106 ÷ 23 = 4 remainder 14 |
| 3 | 23 ÷ 14 = 1 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 159 and 77 | 12243 |
| 130 and 78 | 390 |
| 174 and 156 | 4524 |
| 77 and 59 | 4543 |
| 191 and 45 | 8595 |