Least Common Multiple (LCM) of 109 and 111
The least common multiple (LCM) of 109 and 111 is 12099.
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 109 and 111?
First, calculate the GCD of 109 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 111 = 0 remainder 109 |
| 2 | 111 ÷ 109 = 1 remainder 2 |
| 3 | 109 ÷ 2 = 54 remainder 1 |
| 4 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 11 | 1463 |
| 62 and 187 | 11594 |
| 75 and 145 | 2175 |
| 35 and 121 | 4235 |
| 180 and 184 | 8280 |