Least Common Multiple (LCM) of 195 and 199
The least common multiple (LCM) of 195 and 199 is 38805.
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 195 and 199?
First, calculate the GCD of 195 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 195 ÷ 199 = 0 remainder 195 |
| 2 | 199 ÷ 195 = 1 remainder 4 |
| 3 | 195 ÷ 4 = 48 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 41 | 1517 |
| 61 and 119 | 7259 |
| 51 and 79 | 4029 |
| 76 and 192 | 3648 |
| 139 and 180 | 25020 |