Least Common Multiple (LCM) of 108 and 129
The least common multiple (LCM) of 108 and 129 is 4644.
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 108 and 129?
First, calculate the GCD of 108 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 129 = 0 remainder 108 |
| 2 | 129 ÷ 108 = 1 remainder 21 |
| 3 | 108 ÷ 21 = 5 remainder 3 |
| 4 | 21 ÷ 3 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 62 | 3658 |
| 81 and 115 | 9315 |
| 162 and 91 | 14742 |
| 67 and 129 | 8643 |
| 79 and 26 | 2054 |