Least Common Multiple (LCM) of 114 and 199
The least common multiple (LCM) of 114 and 199 is 22686.
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 114 and 199?
First, calculate the GCD of 114 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 199 = 0 remainder 114 |
| 2 | 199 ÷ 114 = 1 remainder 85 |
| 3 | 114 ÷ 85 = 1 remainder 29 |
| 4 | 85 ÷ 29 = 2 remainder 27 |
| 5 | 29 ÷ 27 = 1 remainder 2 |
| 6 | 27 ÷ 2 = 13 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 31 and 81 | 2511 |
| 44 and 184 | 2024 |
| 143 and 140 | 20020 |
| 197 and 39 | 7683 |
| 84 and 168 | 168 |