Least Common Multiple (LCM) of 83 and 198
The least common multiple (LCM) of 83 and 198 is 16434.
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 83 and 198?
First, calculate the GCD of 83 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 198 = 0 remainder 83 |
| 2 | 198 ÷ 83 = 2 remainder 32 |
| 3 | 83 ÷ 32 = 2 remainder 19 |
| 4 | 32 ÷ 19 = 1 remainder 13 |
| 5 | 19 ÷ 13 = 1 remainder 6 |
| 6 | 13 ÷ 6 = 2 remainder 1 |
| 7 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 122 | 9150 |
| 90 and 65 | 1170 |
| 200 and 157 | 31400 |
| 11 and 97 | 1067 |
| 31 and 81 | 2511 |