Least Common Multiple (LCM) of 89 and 130
The least common multiple (LCM) of 89 and 130 is 11570.
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 89 and 130?
First, calculate the GCD of 89 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 89 ÷ 130 = 0 remainder 89 |
| 2 | 130 ÷ 89 = 1 remainder 41 |
| 3 | 89 ÷ 41 = 2 remainder 7 |
| 4 | 41 ÷ 7 = 5 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 70 | 1260 |
| 142 and 129 | 18318 |
| 33 and 107 | 3531 |
| 93 and 199 | 18507 |
| 126 and 182 | 1638 |