Least Common Multiple (LCM) of 80 and 131
The least common multiple (LCM) of 80 and 131 is 10480.
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 131?
First, calculate the GCD of 80 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 80 ÷ 131 = 0 remainder 80 |
| 2 | 131 ÷ 80 = 1 remainder 51 |
| 3 | 80 ÷ 51 = 1 remainder 29 |
| 4 | 51 ÷ 29 = 1 remainder 22 |
| 5 | 29 ÷ 22 = 1 remainder 7 |
| 6 | 22 ÷ 7 = 3 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 12 | 108 |
| 87 and 108 | 3132 |
| 19 and 63 | 1197 |
| 45 and 68 | 3060 |
| 90 and 65 | 1170 |