Least Common Multiple (LCM) of 199 and 109
The least common multiple (LCM) of 199 and 109 is 21691.
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 199 and 109?
First, calculate the GCD of 199 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 109 = 1 remainder 90 |
| 2 | 109 ÷ 90 = 1 remainder 19 |
| 3 | 90 ÷ 19 = 4 remainder 14 |
| 4 | 19 ÷ 14 = 1 remainder 5 |
| 5 | 14 ÷ 5 = 2 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 85 | 1105 |
| 110 and 105 | 2310 |
| 21 and 137 | 2877 |
| 32 and 196 | 1568 |
| 105 and 81 | 2835 |