Least Common Multiple (LCM) of 136 and 199
The least common multiple (LCM) of 136 and 199 is 27064.
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 136 and 199?
First, calculate the GCD of 136 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 136 ÷ 199 = 0 remainder 136 |
| 2 | 199 ÷ 136 = 1 remainder 63 |
| 3 | 136 ÷ 63 = 2 remainder 10 |
| 4 | 63 ÷ 10 = 6 remainder 3 |
| 5 | 10 ÷ 3 = 3 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 37 | 6105 |
| 86 and 190 | 8170 |
| 105 and 71 | 7455 |
| 195 and 191 | 37245 |
| 47 and 112 | 5264 |