Least Common Multiple (LCM) of 115 and 109
The least common multiple (LCM) of 115 and 109 is 12535.
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 109?
First, calculate the GCD of 115 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 109 = 1 remainder 6 |
| 2 | 109 ÷ 6 = 18 remainder 1 |
| 3 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 74 and 153 | 11322 |
| 31 and 104 | 3224 |
| 35 and 107 | 3745 |
| 116 and 121 | 14036 |
| 77 and 75 | 5775 |