Least Common Multiple (LCM) of 198 and 89
The least common multiple (LCM) of 198 and 89 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 198 and 89?
First, calculate the GCD of 198 and 89 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 89 = 2 remainder 20 |
| 2 | 89 ÷ 20 = 4 remainder 9 |
| 3 | 20 ÷ 9 = 2 remainder 2 |
| 4 | 9 ÷ 2 = 4 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 151 and 118 | 17818 |
| 160 and 76 | 3040 |
| 15 and 61 | 915 |
| 84 and 52 | 1092 |
| 113 and 105 | 11865 |