Least Common Multiple (LCM) of 130 and 180
The least common multiple (LCM) of 130 and 180 is 2340.
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 180?
First, calculate the GCD of 130 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 130 ÷ 180 = 0 remainder 130 |
| 2 | 180 ÷ 130 = 1 remainder 50 |
| 3 | 130 ÷ 50 = 2 remainder 30 |
| 4 | 50 ÷ 30 = 1 remainder 20 |
| 5 | 30 ÷ 20 = 1 remainder 10 |
| 6 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 103 | 1854 |
| 85 and 170 | 170 |
| 48 and 16 | 48 |
| 77 and 153 | 11781 |
| 24 and 190 | 2280 |