Least Common Multiple (LCM) of 199 and 114
The least common multiple (LCM) of 199 and 114 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 199 and 114?
First, calculate the GCD of 199 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 114 = 1 remainder 85 |
| 2 | 114 ÷ 85 = 1 remainder 29 |
| 3 | 85 ÷ 29 = 2 remainder 27 |
| 4 | 29 ÷ 27 = 1 remainder 2 |
| 5 | 27 ÷ 2 = 13 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 79 | 9638 |
| 83 and 69 | 5727 |
| 54 and 12 | 108 |
| 133 and 130 | 17290 |
| 188 and 31 | 5828 |