Least Common Multiple (LCM) of 115 and 108
The least common multiple (LCM) of 115 and 108 is 12420.
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 108?
First, calculate the GCD of 115 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 115 ÷ 108 = 1 remainder 7 |
| 2 | 108 ÷ 7 = 15 remainder 3 |
| 3 | 7 ÷ 3 = 2 remainder 1 |
| 4 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 120 | 5160 |
| 19 and 130 | 2470 |
| 109 and 155 | 16895 |
| 133 and 39 | 5187 |
| 164 and 82 | 164 |