Least Common Multiple (LCM) of 131 and 107
The least common multiple (LCM) of 131 and 107 is 14017.
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 131 and 107?
First, calculate the GCD of 131 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 107 = 1 remainder 24 |
| 2 | 107 ÷ 24 = 4 remainder 11 |
| 3 | 24 ÷ 11 = 2 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 131 and 83 | 10873 |
| 54 and 130 | 3510 |
| 81 and 29 | 2349 |
| 80 and 17 | 1360 |
| 65 and 38 | 2470 |