Least Common Multiple (LCM) of 108 and 180
The least common multiple (LCM) of 108 and 180 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 108 and 180?
First, calculate the GCD of 108 and 180 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 180 = 0 remainder 108 |
| 2 | 180 ÷ 108 = 1 remainder 72 |
| 3 | 108 ÷ 72 = 1 remainder 36 |
| 4 | 72 ÷ 36 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 29 and 59 | 1711 |
| 87 and 144 | 4176 |
| 60 and 60 | 60 |
| 56 and 32 | 224 |
| 182 and 169 | 2366 |