Least Common Multiple (LCM) of 83 and 199
The least common multiple (LCM) of 83 and 199 is 16517.
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 199?
First, calculate the GCD of 83 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 83 ÷ 199 = 0 remainder 83 |
| 2 | 199 ÷ 83 = 2 remainder 33 |
| 3 | 83 ÷ 33 = 2 remainder 17 |
| 4 | 33 ÷ 17 = 1 remainder 16 |
| 5 | 17 ÷ 16 = 1 remainder 1 |
| 6 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 43 and 88 | 3784 |
| 20 and 50 | 100 |
| 176 and 185 | 32560 |
| 115 and 84 | 9660 |
| 142 and 48 | 3408 |