Least Common Multiple (LCM) of 80 and 110
The least common multiple (LCM) of 80 and 110 is 880.
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 110?
First, calculate the GCD of 80 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 110 = 0 remainder 80 |
| 2 | 110 ÷ 80 = 1 remainder 30 |
| 3 | 80 ÷ 30 = 2 remainder 20 |
| 4 | 30 ÷ 20 = 1 remainder 10 |
| 5 | 20 ÷ 10 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 100 | 6900 |
| 188 and 109 | 20492 |
| 182 and 82 | 7462 |
| 99 and 48 | 1584 |
| 42 and 55 | 2310 |