Least Common Multiple (LCM) of 115 and 194
The least common multiple (LCM) of 115 and 194 is 22310.
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 194?
First, calculate the GCD of 115 and 194 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 194 = 0 remainder 115 |
| 2 | 194 ÷ 115 = 1 remainder 79 |
| 3 | 115 ÷ 79 = 1 remainder 36 |
| 4 | 79 ÷ 36 = 2 remainder 7 |
| 5 | 36 ÷ 7 = 5 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 73 | 12410 |
| 69 and 103 | 7107 |
| 33 and 150 | 1650 |
| 54 and 196 | 5292 |
| 37 and 173 | 6401 |