Least Common Multiple (LCM) of 114 and 186
The least common multiple (LCM) of 114 and 186 is 3534.
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 186?
First, calculate the GCD of 114 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 186 = 0 remainder 114 |
| 2 | 186 ÷ 114 = 1 remainder 72 |
| 3 | 114 ÷ 72 = 1 remainder 42 |
| 4 | 72 ÷ 42 = 1 remainder 30 |
| 5 | 42 ÷ 30 = 1 remainder 12 |
| 6 | 30 ÷ 12 = 2 remainder 6 |
| 7 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 51 | 714 |
| 181 and 99 | 17919 |
| 108 and 131 | 14148 |
| 66 and 156 | 1716 |
| 155 and 199 | 30845 |