Least Common Multiple (LCM) of 80 and 109
The least common multiple (LCM) of 80 and 109 is 8720.
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 109?
First, calculate the GCD of 80 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 109 = 0 remainder 80 |
| 2 | 109 ÷ 80 = 1 remainder 29 |
| 3 | 80 ÷ 29 = 2 remainder 22 |
| 4 | 29 ÷ 22 = 1 remainder 7 |
| 5 | 22 ÷ 7 = 3 remainder 1 |
| 6 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 18 | 2070 |
| 193 and 88 | 16984 |
| 34 and 34 | 34 |
| 42 and 20 | 420 |
| 190 and 143 | 27170 |