Least Common Multiple (LCM) of 189 and 130
The least common multiple (LCM) of 189 and 130 is 24570.
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 130?
First, calculate the GCD of 189 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 189 ÷ 130 = 1 remainder 59 |
| 2 | 130 ÷ 59 = 2 remainder 12 |
| 3 | 59 ÷ 12 = 4 remainder 11 |
| 4 | 12 ÷ 11 = 1 remainder 1 |
| 5 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 54 | 4644 |
| 49 and 159 | 7791 |
| 46 and 105 | 4830 |
| 83 and 29 | 2407 |
| 12 and 61 | 732 |