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 |
|---|---|
| 130 and 67 | 8710 |
| 92 and 163 | 14996 |
| 126 and 19 | 2394 |
| 104 and 103 | 10712 |
| 79 and 95 | 7505 |