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 |
|---|---|
| 65 and 109 | 7085 |
| 89 and 13 | 1157 |
| 13 and 68 | 884 |
| 170 and 100 | 1700 |
| 114 and 67 | 7638 |