Least Common Multiple (LCM) of 80 and 127
The least common multiple (LCM) of 80 and 127 is 10160.
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 127?
First, calculate the GCD of 80 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 127 = 0 remainder 80 |
| 2 | 127 ÷ 80 = 1 remainder 47 |
| 3 | 80 ÷ 47 = 1 remainder 33 |
| 4 | 47 ÷ 33 = 1 remainder 14 |
| 5 | 33 ÷ 14 = 2 remainder 5 |
| 6 | 14 ÷ 5 = 2 remainder 4 |
| 7 | 5 ÷ 4 = 1 remainder 1 |
| 8 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 120 and 24 | 120 |
| 116 and 114 | 6612 |
| 174 and 129 | 7482 |
| 20 and 43 | 860 |
| 79 and 189 | 14931 |