Least Common Multiple (LCM) of 199 and 83
The least common multiple (LCM) of 199 and 83 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 199 and 83?
First, calculate the GCD of 199 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 83 = 2 remainder 33 |
| 2 | 83 ÷ 33 = 2 remainder 17 |
| 3 | 33 ÷ 17 = 1 remainder 16 |
| 4 | 17 ÷ 16 = 1 remainder 1 |
| 5 | 16 ÷ 1 = 16 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 24 | 600 |
| 112 and 132 | 3696 |
| 52 and 109 | 5668 |
| 141 and 164 | 23124 |
| 141 and 159 | 7473 |