Least Common Multiple (LCM) of 80 and 107
The least common multiple (LCM) of 80 and 107 is 8560.
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 107?
First, calculate the GCD of 80 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 107 = 0 remainder 80 |
| 2 | 107 ÷ 80 = 1 remainder 27 |
| 3 | 80 ÷ 27 = 2 remainder 26 |
| 4 | 27 ÷ 26 = 1 remainder 1 |
| 5 | 26 ÷ 1 = 26 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 165 and 112 | 18480 |
| 145 and 157 | 22765 |
| 127 and 59 | 7493 |
| 180 and 169 | 30420 |
| 76 and 129 | 9804 |