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 |
|---|---|
| 46 and 140 | 3220 |
| 53 and 20 | 1060 |
| 171 and 117 | 2223 |
| 121 and 96 | 11616 |
| 172 and 114 | 9804 |