Least Common Multiple (LCM) of 80 and 108
The least common multiple (LCM) of 80 and 108 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 80 and 108?
First, calculate the GCD of 80 and 108 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 108 = 0 remainder 80 |
| 2 | 108 ÷ 80 = 1 remainder 28 |
| 3 | 80 ÷ 28 = 2 remainder 24 |
| 4 | 28 ÷ 24 = 1 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 149 | 15943 |
| 113 and 120 | 13560 |
| 146 and 115 | 16790 |
| 33 and 193 | 6369 |
| 80 and 62 | 2480 |