Least Common Multiple (LCM) of 197 and 83
The least common multiple (LCM) of 197 and 83 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 197 and 83?
First, calculate the GCD of 197 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 197 ÷ 83 = 2 remainder 31 |
| 2 | 83 ÷ 31 = 2 remainder 21 |
| 3 | 31 ÷ 21 = 1 remainder 10 |
| 4 | 21 ÷ 10 = 2 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 53 and 23 | 1219 |
| 154 and 25 | 3850 |
| 53 and 10 | 530 |
| 199 and 48 | 9552 |
| 200 and 71 | 14200 |