Least Common Multiple (LCM) of 114 and 131
The least common multiple (LCM) of 114 and 131 is 14934.
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 131?
First, calculate the GCD of 114 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 114 ÷ 131 = 0 remainder 114 |
| 2 | 131 ÷ 114 = 1 remainder 17 |
| 3 | 114 ÷ 17 = 6 remainder 12 |
| 4 | 17 ÷ 12 = 1 remainder 5 |
| 5 | 12 ÷ 5 = 2 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 97 | 16975 |
| 35 and 183 | 6405 |
| 180 and 193 | 34740 |
| 172 and 42 | 3612 |
| 119 and 187 | 1309 |