Least Common Multiple (LCM) of 108 and 109
The least common multiple (LCM) of 108 and 109 is 11772.
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 109?
First, calculate the GCD of 108 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 109 = 0 remainder 108 |
| 2 | 109 ÷ 108 = 1 remainder 1 |
| 3 | 108 ÷ 1 = 108 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 148 | 15244 |
| 180 and 89 | 16020 |
| 107 and 199 | 21293 |
| 172 and 116 | 4988 |
| 200 and 127 | 25400 |