Least Common Multiple (LCM) of 109 and 199
The least common multiple (LCM) of 109 and 199 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 109 and 199?
First, calculate the GCD of 109 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 199 = 0 remainder 109 |
| 2 | 199 ÷ 109 = 1 remainder 90 |
| 3 | 109 ÷ 90 = 1 remainder 19 |
| 4 | 90 ÷ 19 = 4 remainder 14 |
| 5 | 19 ÷ 14 = 1 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 142 | 19170 |
| 54 and 60 | 540 |
| 20 and 85 | 340 |
| 62 and 98 | 3038 |
| 29 and 100 | 2900 |