Least Common Multiple (LCM) of 198 and 83
The least common multiple (LCM) of 198 and 83 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 198 and 83?
First, calculate the GCD of 198 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 83 = 2 remainder 32 |
| 2 | 83 ÷ 32 = 2 remainder 19 |
| 3 | 32 ÷ 19 = 1 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 148 | 10508 |
| 45 and 80 | 720 |
| 140 and 71 | 9940 |
| 53 and 52 | 2756 |
| 82 and 95 | 7790 |