Least Common Multiple (LCM) of 194 and 199
The least common multiple (LCM) of 194 and 199 is 38606.
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 199?
First, calculate the GCD of 194 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 194 ÷ 199 = 0 remainder 194 |
| 2 | 199 ÷ 194 = 1 remainder 5 |
| 3 | 194 ÷ 5 = 38 remainder 4 |
| 4 | 5 ÷ 4 = 1 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 116 and 105 | 12180 |
| 137 and 107 | 14659 |
| 139 and 100 | 13900 |
| 149 and 107 | 15943 |
| 135 and 39 | 1755 |