Least Common Multiple (LCM) of 194 and 109
The least common multiple (LCM) of 194 and 109 is 21146.
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 194 and 109?
First, calculate the GCD of 194 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 109 = 1 remainder 85 |
| 2 | 109 ÷ 85 = 1 remainder 24 |
| 3 | 85 ÷ 24 = 3 remainder 13 |
| 4 | 24 ÷ 13 = 1 remainder 11 |
| 5 | 13 ÷ 11 = 1 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 25 | 3675 |
| 187 and 100 | 18700 |
| 101 and 60 | 6060 |
| 94 and 142 | 6674 |
| 35 and 52 | 1820 |