Least Common Multiple (LCM) of 115 and 199
The least common multiple (LCM) of 115 and 199 is 22885.
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 115 and 199?
First, calculate the GCD of 115 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 199 = 0 remainder 115 |
| 2 | 199 ÷ 115 = 1 remainder 84 |
| 3 | 115 ÷ 84 = 1 remainder 31 |
| 4 | 84 ÷ 31 = 2 remainder 22 |
| 5 | 31 ÷ 22 = 1 remainder 9 |
| 6 | 22 ÷ 9 = 2 remainder 4 |
| 7 | 9 ÷ 4 = 2 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 162 | 6966 |
| 65 and 153 | 9945 |
| 21 and 86 | 1806 |
| 86 and 168 | 7224 |
| 146 and 163 | 23798 |