Least Common Multiple (LCM) of 191 and 111
The least common multiple (LCM) of 191 and 111 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 191 and 111?
First, calculate the GCD of 191 and 111 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 191 ÷ 111 = 1 remainder 80 |
| 2 | 111 ÷ 80 = 1 remainder 31 |
| 3 | 80 ÷ 31 = 2 remainder 18 |
| 4 | 31 ÷ 18 = 1 remainder 13 |
| 5 | 18 ÷ 13 = 1 remainder 5 |
| 6 | 13 ÷ 5 = 2 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 174 and 145 | 870 |
| 17 and 163 | 2771 |
| 72 and 28 | 504 |
| 147 and 115 | 16905 |
| 100 and 84 | 2100 |