Least Common Multiple (LCM) of 111 and 191
The least common multiple (LCM) of 111 and 191 is 21201.
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 191?
First, calculate the GCD of 111 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 111 ÷ 191 = 0 remainder 111 |
| 2 | 191 ÷ 111 = 1 remainder 80 |
| 3 | 111 ÷ 80 = 1 remainder 31 |
| 4 | 80 ÷ 31 = 2 remainder 18 |
| 5 | 31 ÷ 18 = 1 remainder 13 |
| 6 | 18 ÷ 13 = 1 remainder 5 |
| 7 | 13 ÷ 5 = 2 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 21 | 525 |
| 143 and 185 | 26455 |
| 164 and 76 | 3116 |
| 159 and 97 | 15423 |
| 131 and 51 | 6681 |