Least Common Multiple (LCM) of 180 and 130
The least common multiple (LCM) of 180 and 130 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 180 and 130?
First, calculate the GCD of 180 and 130 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 130 = 1 remainder 50 |
| 2 | 130 ÷ 50 = 2 remainder 30 |
| 3 | 50 ÷ 30 = 1 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 186 | 21390 |
| 110 and 101 | 11110 |
| 199 and 12 | 2388 |
| 109 and 143 | 15587 |
| 23 and 30 | 690 |