Least Common Multiple (LCM) of 199 and 115
The least common multiple (LCM) of 199 and 115 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 199 and 115?
First, calculate the GCD of 199 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 199 ÷ 115 = 1 remainder 84 |
| 2 | 115 ÷ 84 = 1 remainder 31 |
| 3 | 84 ÷ 31 = 2 remainder 22 |
| 4 | 31 ÷ 22 = 1 remainder 9 |
| 5 | 22 ÷ 9 = 2 remainder 4 |
| 6 | 9 ÷ 4 = 2 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 55 and 69 | 3795 |
| 110 and 178 | 9790 |
| 169 and 76 | 12844 |
| 101 and 109 | 11009 |
| 153 and 124 | 18972 |