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 |
|---|---|
| 85 and 15 | 255 |
| 153 and 121 | 18513 |
| 100 and 163 | 16300 |
| 37 and 160 | 5920 |
| 47 and 169 | 7943 |