Least Common Multiple (LCM) of 89 and 198
The least common multiple (LCM) of 89 and 198 is 17622.
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 89 and 198?
First, calculate the GCD of 89 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 198 = 0 remainder 89 |
| 2 | 198 ÷ 89 = 2 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 |
|---|---|
| 122 and 62 | 3782 |
| 139 and 148 | 20572 |
| 189 and 140 | 3780 |
| 75 and 25 | 75 |
| 200 and 53 | 10600 |