Least Common Multiple (LCM) of 114 and 194
The least common multiple (LCM) of 114 and 194 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 114 and 194?
First, calculate the GCD of 114 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 194 = 0 remainder 114 |
| 2 | 194 ÷ 114 = 1 remainder 80 |
| 3 | 114 ÷ 80 = 1 remainder 34 |
| 4 | 80 ÷ 34 = 2 remainder 12 |
| 5 | 34 ÷ 12 = 2 remainder 10 |
| 6 | 12 ÷ 10 = 1 remainder 2 |
| 7 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 165 | 8085 |
| 154 and 65 | 10010 |
| 75 and 195 | 975 |
| 73 and 141 | 10293 |
| 83 and 79 | 6557 |