Least Common Multiple (LCM) of 83 and 193
The least common multiple (LCM) of 83 and 193 is 16019.
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 193?
First, calculate the GCD of 83 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 193 = 0 remainder 83 |
| 2 | 193 ÷ 83 = 2 remainder 27 |
| 3 | 83 ÷ 27 = 3 remainder 2 |
| 4 | 27 ÷ 2 = 13 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 34 | 646 |
| 189 and 162 | 1134 |
| 85 and 113 | 9605 |
| 165 and 11 | 165 |
| 109 and 52 | 5668 |