Least Common Multiple (LCM) of 115 and 195
The least common multiple (LCM) of 115 and 195 is 4485.
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 195?
First, calculate the GCD of 115 and 195 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 195 = 0 remainder 115 |
| 2 | 195 ÷ 115 = 1 remainder 80 |
| 3 | 115 ÷ 80 = 1 remainder 35 |
| 4 | 80 ÷ 35 = 2 remainder 10 |
| 5 | 35 ÷ 10 = 3 remainder 5 |
| 6 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 106 | 1272 |
| 149 and 13 | 1937 |
| 97 and 199 | 19303 |
| 108 and 189 | 756 |
| 128 and 165 | 21120 |