Least Common Multiple (LCM) of 188 and 111
The least common multiple (LCM) of 188 and 111 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 188 and 111?
First, calculate the GCD of 188 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 111 = 1 remainder 77 |
| 2 | 111 ÷ 77 = 1 remainder 34 |
| 3 | 77 ÷ 34 = 2 remainder 9 |
| 4 | 34 ÷ 9 = 3 remainder 7 |
| 5 | 9 ÷ 7 = 1 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 198 and 117 | 2574 |
| 102 and 142 | 7242 |
| 103 and 146 | 15038 |
| 189 and 17 | 3213 |
| 58 and 66 | 1914 |