Least Common Multiple (LCM) of 180 and 108
The least common multiple (LCM) of 180 and 108 is 540.
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 108?
First, calculate the GCD of 180 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 180 ÷ 108 = 1 remainder 72 |
| 2 | 108 ÷ 72 = 1 remainder 36 |
| 3 | 72 ÷ 36 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 83 | 10209 |
| 22 and 111 | 2442 |
| 62 and 109 | 6758 |
| 103 and 195 | 20085 |
| 110 and 103 | 11330 |