Least Common Multiple (LCM) of 198 and 109
The least common multiple (LCM) of 198 and 109 is 21582.
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 198 and 109?
First, calculate the GCD of 198 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 109 = 1 remainder 89 |
| 2 | 109 ÷ 89 = 1 remainder 20 |
| 3 | 89 ÷ 20 = 4 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 |
|---|---|
| 144 and 93 | 4464 |
| 186 and 136 | 12648 |
| 40 and 133 | 5320 |
| 85 and 108 | 9180 |
| 96 and 103 | 9888 |