Least Common Multiple (LCM) of 80 and 129
The least common multiple (LCM) of 80 and 129 is 10320.
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 129?
First, calculate the GCD of 80 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 129 = 0 remainder 80 |
| 2 | 129 ÷ 80 = 1 remainder 49 |
| 3 | 80 ÷ 49 = 1 remainder 31 |
| 4 | 49 ÷ 31 = 1 remainder 18 |
| 5 | 31 ÷ 18 = 1 remainder 13 |
| 6 | 18 ÷ 13 = 1 remainder 5 |
| 7 | 13 ÷ 5 = 2 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 176 | 19184 |
| 68 and 180 | 3060 |
| 114 and 190 | 570 |
| 185 and 50 | 1850 |
| 92 and 45 | 4140 |