Least Common Multiple (LCM) of 119 and 199
The least common multiple (LCM) of 119 and 199 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 119 and 199?
First, calculate the GCD of 119 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 119 ÷ 199 = 0 remainder 119 |
| 2 | 199 ÷ 119 = 1 remainder 80 |
| 3 | 119 ÷ 80 = 1 remainder 39 |
| 4 | 80 ÷ 39 = 2 remainder 2 |
| 5 | 39 ÷ 2 = 19 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 63 and 112 | 1008 |
| 104 and 188 | 4888 |
| 96 and 136 | 1632 |
| 160 and 58 | 4640 |
| 21 and 36 | 252 |