Least Common Multiple (LCM) of 109 and 194
The least common multiple (LCM) of 109 and 194 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 109 and 194?
First, calculate the GCD of 109 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 109 ÷ 194 = 0 remainder 109 |
| 2 | 194 ÷ 109 = 1 remainder 85 |
| 3 | 109 ÷ 85 = 1 remainder 24 |
| 4 | 85 ÷ 24 = 3 remainder 13 |
| 5 | 24 ÷ 13 = 1 remainder 11 |
| 6 | 13 ÷ 11 = 1 remainder 2 |
| 7 | 11 ÷ 2 = 5 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 69 and 46 | 138 |
| 111 and 96 | 3552 |
| 151 and 135 | 20385 |
| 78 and 89 | 6942 |
| 108 and 52 | 1404 |