Least Common Multiple (LCM) of 114 and 115
The least common multiple (LCM) of 114 and 115 is 13110.
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 114 and 115?
First, calculate the GCD of 114 and 115 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 115 = 0 remainder 114 |
| 2 | 115 ÷ 114 = 1 remainder 1 |
| 3 | 114 ÷ 1 = 114 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 137 and 10 | 1370 |
| 103 and 199 | 20497 |
| 105 and 169 | 17745 |
| 25 and 137 | 3425 |
| 125 and 76 | 9500 |