Least Common Multiple (LCM) of 115 and 107
The least common multiple (LCM) of 115 and 107 is 12305.
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 107?
First, calculate the GCD of 115 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 107 = 1 remainder 8 |
| 2 | 107 ÷ 8 = 13 remainder 3 |
| 3 | 8 ÷ 3 = 2 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 165 | 9405 |
| 55 and 179 | 9845 |
| 105 and 112 | 1680 |
| 101 and 180 | 18180 |
| 91 and 51 | 4641 |