Least Common Multiple (LCM) of 186 and 111
The least common multiple (LCM) of 186 and 111 is 6882.
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 186 and 111?
First, calculate the GCD of 186 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 186 ÷ 111 = 1 remainder 75 |
| 2 | 111 ÷ 75 = 1 remainder 36 |
| 3 | 75 ÷ 36 = 2 remainder 3 |
| 4 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 97 and 37 | 3589 |
| 100 and 42 | 2100 |
| 20 and 136 | 680 |
| 33 and 49 | 1617 |
| 200 and 149 | 29800 |