Least Common Multiple (LCM) of 111 and 19
The least common multiple (LCM) of 111 and 19 is 2109.
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 19?
First, calculate the GCD of 111 and 19 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 19 = 5 remainder 16 |
| 2 | 19 ÷ 16 = 1 remainder 3 |
| 3 | 16 ÷ 3 = 5 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 105 and 95 | 1995 |
| 100 and 78 | 3900 |
| 61 and 188 | 11468 |
| 150 and 173 | 25950 |
| 186 and 83 | 15438 |