Least Common Multiple (LCM) of 199 and 119
The least common multiple (LCM) of 199 and 119 is 23681.
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 199 and 119?
First, calculate the GCD of 199 and 119 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 119 = 1 remainder 80 |
| 2 | 119 ÷ 80 = 1 remainder 39 |
| 3 | 80 ÷ 39 = 2 remainder 2 |
| 4 | 39 ÷ 2 = 19 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 85 and 85 | 85 |
| 117 and 134 | 15678 |
| 19 and 14 | 266 |
| 41 and 37 | 1517 |
| 172 and 17 | 2924 |