Least Common Multiple (LCM) of 109 and 191
The least common multiple (LCM) of 109 and 191 is 20819.
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 109 and 191?
First, calculate the GCD of 109 and 191 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 191 = 0 remainder 109 |
| 2 | 191 ÷ 109 = 1 remainder 82 |
| 3 | 109 ÷ 82 = 1 remainder 27 |
| 4 | 82 ÷ 27 = 3 remainder 1 |
| 5 | 27 ÷ 1 = 27 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 60 | 2580 |
| 180 and 15 | 180 |
| 152 and 109 | 16568 |
| 45 and 187 | 8415 |
| 90 and 138 | 2070 |