Least Common Multiple (LCM) of 187 and 111
The least common multiple (LCM) of 187 and 111 is 20757.
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 187 and 111?
First, calculate the GCD of 187 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 187 ÷ 111 = 1 remainder 76 |
| 2 | 111 ÷ 76 = 1 remainder 35 |
| 3 | 76 ÷ 35 = 2 remainder 6 |
| 4 | 35 ÷ 6 = 5 remainder 5 |
| 5 | 6 ÷ 5 = 1 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 110 and 120 | 1320 |
| 48 and 120 | 240 |
| 25 and 112 | 2800 |
| 23 and 194 | 4462 |
| 154 and 83 | 12782 |