Least Common Multiple (LCM) of 194 and 114
The least common multiple (LCM) of 194 and 114 is 11058.
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 194 and 114?
First, calculate the GCD of 194 and 114 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 114 = 1 remainder 80 |
| 2 | 114 ÷ 80 = 1 remainder 34 |
| 3 | 80 ÷ 34 = 2 remainder 12 |
| 4 | 34 ÷ 12 = 2 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 105 | 3045 |
| 100 and 168 | 4200 |
| 187 and 186 | 34782 |
| 135 and 122 | 16470 |
| 22 and 17 | 374 |