Least Common Multiple (LCM) of 115 and 193
The least common multiple (LCM) of 115 and 193 is 22195.
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 193?
First, calculate the GCD of 115 and 193 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 193 = 0 remainder 115 |
| 2 | 193 ÷ 115 = 1 remainder 78 |
| 3 | 115 ÷ 78 = 1 remainder 37 |
| 4 | 78 ÷ 37 = 2 remainder 4 |
| 5 | 37 ÷ 4 = 9 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 53 | 1961 |
| 37 and 90 | 3330 |
| 56 and 148 | 2072 |
| 33 and 158 | 5214 |
| 21 and 35 | 105 |