Least Common Multiple (LCM) of 107 and 131
The least common multiple (LCM) of 107 and 131 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 107 and 131?
First, calculate the GCD of 107 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 131 = 0 remainder 107 |
| 2 | 131 ÷ 107 = 1 remainder 24 |
| 3 | 107 ÷ 24 = 4 remainder 11 |
| 4 | 24 ÷ 11 = 2 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 170 and 136 | 680 |
| 28 and 73 | 2044 |
| 174 and 23 | 4002 |
| 49 and 162 | 7938 |
| 120 and 180 | 360 |