Least Common Multiple (LCM) of 189 and 131
The least common multiple (LCM) of 189 and 131 is 24759.
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 189 and 131?
First, calculate the GCD of 189 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 131 = 1 remainder 58 |
| 2 | 131 ÷ 58 = 2 remainder 15 |
| 3 | 58 ÷ 15 = 3 remainder 13 |
| 4 | 15 ÷ 13 = 1 remainder 2 |
| 5 | 13 ÷ 2 = 6 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 180 and 155 | 5580 |
| 84 and 99 | 2772 |
| 78 and 97 | 7566 |
| 11 and 113 | 1243 |
| 145 and 29 | 145 |