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 |
|---|---|
| 23 and 26 | 598 |
| 82 and 64 | 2624 |
| 112 and 40 | 560 |
| 31 and 186 | 186 |
| 33 and 31 | 1023 |