Least Common Multiple (LCM) of 108 and 131
The least common multiple (LCM) of 108 and 131 is 14148.
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 108 and 131?
First, calculate the GCD of 108 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 131 = 0 remainder 108 |
| 2 | 131 ÷ 108 = 1 remainder 23 |
| 3 | 108 ÷ 23 = 4 remainder 16 |
| 4 | 23 ÷ 16 = 1 remainder 7 |
| 5 | 16 ÷ 7 = 2 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 80 and 105 | 1680 |
| 53 and 49 | 2597 |
| 126 and 144 | 1008 |
| 128 and 90 | 5760 |
| 183 and 156 | 9516 |