Least Common Multiple (LCM) of 130 and 189
The least common multiple (LCM) of 130 and 189 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 130 and 189?
First, calculate the GCD of 130 and 189 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 189 = 0 remainder 130 |
| 2 | 189 ÷ 130 = 1 remainder 59 |
| 3 | 130 ÷ 59 = 2 remainder 12 |
| 4 | 59 ÷ 12 = 4 remainder 11 |
| 5 | 12 ÷ 11 = 1 remainder 1 |
| 6 | 11 ÷ 1 = 11 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 70 and 38 | 1330 |
| 36 and 178 | 3204 |
| 136 and 136 | 136 |
| 193 and 34 | 6562 |
| 35 and 21 | 105 |