Least Common Multiple (LCM) of 131 and 189
The least common multiple (LCM) of 131 and 189 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 131 and 189?
First, calculate the GCD of 131 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 131 ÷ 189 = 0 remainder 131 |
| 2 | 189 ÷ 131 = 1 remainder 58 |
| 3 | 131 ÷ 58 = 2 remainder 15 |
| 4 | 58 ÷ 15 = 3 remainder 13 |
| 5 | 15 ÷ 13 = 1 remainder 2 |
| 6 | 13 ÷ 2 = 6 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 83 | 1577 |
| 192 and 92 | 4416 |
| 40 and 21 | 840 |
| 87 and 147 | 4263 |
| 48 and 35 | 1680 |