Least Common Multiple (LCM) of 108 and 111
The least common multiple (LCM) of 108 and 111 is 3996.
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 108 and 111?
First, calculate the GCD of 108 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 111 = 0 remainder 108 |
| 2 | 111 ÷ 108 = 1 remainder 3 |
| 3 | 108 ÷ 3 = 36 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 146 | 17082 |
| 123 and 189 | 7749 |
| 147 and 156 | 7644 |
| 169 and 28 | 4732 |
| 27 and 120 | 1080 |