Least Common Multiple (LCM) of 114 and 181
The least common multiple (LCM) of 114 and 181 is 20634.
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 181?
First, calculate the GCD of 114 and 181 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 181 = 0 remainder 114 |
| 2 | 181 ÷ 114 = 1 remainder 67 |
| 3 | 114 ÷ 67 = 1 remainder 47 |
| 4 | 67 ÷ 47 = 1 remainder 20 |
| 5 | 47 ÷ 20 = 2 remainder 7 |
| 6 | 20 ÷ 7 = 2 remainder 6 |
| 7 | 7 ÷ 6 = 1 remainder 1 |
| 8 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 187 and 165 | 2805 |
| 95 and 145 | 2755 |
| 163 and 190 | 30970 |
| 16 and 21 | 336 |
| 100 and 135 | 2700 |