Least Common Multiple (LCM) of 109 and 129
The least common multiple (LCM) of 109 and 129 is 14061.
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 109 and 129?
First, calculate the GCD of 109 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 129 = 0 remainder 109 |
| 2 | 129 ÷ 109 = 1 remainder 20 |
| 3 | 109 ÷ 20 = 5 remainder 9 |
| 4 | 20 ÷ 9 = 2 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 104 and 188 | 4888 |
| 74 and 91 | 6734 |
| 90 and 30 | 90 |
| 135 and 19 | 2565 |
| 77 and 101 | 7777 |