Least Common Multiple (LCM) of 111 and 190
The least common multiple (LCM) of 111 and 190 is 21090.
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 190?
First, calculate the GCD of 111 and 190 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 190 = 0 remainder 111 |
| 2 | 190 ÷ 111 = 1 remainder 79 |
| 3 | 111 ÷ 79 = 1 remainder 32 |
| 4 | 79 ÷ 32 = 2 remainder 15 |
| 5 | 32 ÷ 15 = 2 remainder 2 |
| 6 | 15 ÷ 2 = 7 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 35 | 4970 |
| 162 and 188 | 15228 |
| 105 and 45 | 315 |
| 157 and 83 | 13031 |
| 118 and 74 | 4366 |