Least Common Multiple (LCM) of 200 and 114
The least common multiple (LCM) of 200 and 114 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 200 and 114?
First, calculate the GCD of 200 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 200 ÷ 114 = 1 remainder 86 |
| 2 | 114 ÷ 86 = 1 remainder 28 |
| 3 | 86 ÷ 28 = 3 remainder 2 |
| 4 | 28 ÷ 2 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 99 and 108 | 1188 |
| 77 and 131 | 10087 |
| 195 and 80 | 3120 |
| 125 and 196 | 24500 |
| 177 and 68 | 12036 |