Least Common Multiple (LCM) of 114 and 185
The least common multiple (LCM) of 114 and 185 is 21090.
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 185?
First, calculate the GCD of 114 and 185 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 185 = 0 remainder 114 |
| 2 | 185 ÷ 114 = 1 remainder 71 |
| 3 | 114 ÷ 71 = 1 remainder 43 |
| 4 | 71 ÷ 43 = 1 remainder 28 |
| 5 | 43 ÷ 28 = 1 remainder 15 |
| 6 | 28 ÷ 15 = 1 remainder 13 |
| 7 | 15 ÷ 13 = 1 remainder 2 |
| 8 | 13 ÷ 2 = 6 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 29 | 4466 |
| 30 and 44 | 660 |
| 189 and 85 | 16065 |
| 146 and 17 | 2482 |
| 25 and 18 | 450 |