Least Common Multiple (LCM) of 114 and 200
The least common multiple (LCM) of 114 and 200 is 11400.
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 200?
First, calculate the GCD of 114 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 200 = 0 remainder 114 |
| 2 | 200 ÷ 114 = 1 remainder 86 |
| 3 | 114 ÷ 86 = 1 remainder 28 |
| 4 | 86 ÷ 28 = 3 remainder 2 |
| 5 | 28 ÷ 2 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 83 and 31 | 2573 |
| 37 and 190 | 7030 |
| 17 and 56 | 952 |
| 106 and 177 | 18762 |
| 45 and 165 | 495 |