Least Common Multiple (LCM) of 108 and 80
The least common multiple (LCM) of 108 and 80 is 2160.
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 80?
First, calculate the GCD of 108 and 80 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 80 = 1 remainder 28 |
| 2 | 80 ÷ 28 = 2 remainder 24 |
| 3 | 28 ÷ 24 = 1 remainder 4 |
| 4 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 73 and 96 | 7008 |
| 38 and 77 | 2926 |
| 199 and 41 | 8159 |
| 68 and 15 | 1020 |
| 12 and 53 | 636 |