Least Common Multiple (LCM) of 109 and 198
The least common multiple (LCM) of 109 and 198 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 109 and 198?
First, calculate the GCD of 109 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 198 = 0 remainder 109 |
| 2 | 198 ÷ 109 = 1 remainder 89 |
| 3 | 109 ÷ 89 = 1 remainder 20 |
| 4 | 89 ÷ 20 = 4 remainder 9 |
| 5 | 20 ÷ 9 = 2 remainder 2 |
| 6 | 9 ÷ 2 = 4 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 77 | 1309 |
| 135 and 68 | 9180 |
| 21 and 64 | 1344 |
| 183 and 118 | 21594 |
| 65 and 183 | 11895 |