Least Common Multiple (LCM) of 111 and 188
The least common multiple (LCM) of 111 and 188 is 20868.
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 188?
First, calculate the GCD of 111 and 188 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 188 = 0 remainder 111 |
| 2 | 188 ÷ 111 = 1 remainder 77 |
| 3 | 111 ÷ 77 = 1 remainder 34 |
| 4 | 77 ÷ 34 = 2 remainder 9 |
| 5 | 34 ÷ 9 = 3 remainder 7 |
| 6 | 9 ÷ 7 = 1 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 112 | 7504 |
| 75 and 141 | 3525 |
| 109 and 161 | 17549 |
| 10 and 89 | 890 |
| 165 and 178 | 29370 |