Least Common Multiple (LCM) of 111 and 186
The least common multiple (LCM) of 111 and 186 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 111 and 186?
First, calculate the GCD of 111 and 186 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 186 = 0 remainder 111 |
| 2 | 186 ÷ 111 = 1 remainder 75 |
| 3 | 111 ÷ 75 = 1 remainder 36 |
| 4 | 75 ÷ 36 = 2 remainder 3 |
| 5 | 36 ÷ 3 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 149 | 21009 |
| 42 and 61 | 2562 |
| 138 and 88 | 6072 |
| 63 and 12 | 252 |
| 104 and 149 | 15496 |