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 |
|---|---|
| 124 and 74 | 4588 |
| 137 and 178 | 24386 |
| 143 and 42 | 6006 |
| 113 and 180 | 20340 |
| 90 and 20 | 180 |