Least Common Multiple (LCM) of 83 and 197
The least common multiple (LCM) of 83 and 197 is 16351.
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 197?
First, calculate the GCD of 83 and 197 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 197 = 0 remainder 83 |
| 2 | 197 ÷ 83 = 2 remainder 31 |
| 3 | 83 ÷ 31 = 2 remainder 21 |
| 4 | 31 ÷ 21 = 1 remainder 10 |
| 5 | 21 ÷ 10 = 2 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 75 | 675 |
| 186 and 38 | 3534 |
| 96 and 51 | 1632 |
| 75 and 196 | 14700 |
| 51 and 31 | 1581 |