Least Common Multiple (LCM) of 81 and 131
The least common multiple (LCM) of 81 and 131 is 10611.
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 81 and 131?
First, calculate the GCD of 81 and 131 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 131 = 0 remainder 81 |
| 2 | 131 ÷ 81 = 1 remainder 50 |
| 3 | 81 ÷ 50 = 1 remainder 31 |
| 4 | 50 ÷ 31 = 1 remainder 19 |
| 5 | 31 ÷ 19 = 1 remainder 12 |
| 6 | 19 ÷ 12 = 1 remainder 7 |
| 7 | 12 ÷ 7 = 1 remainder 5 |
| 8 | 7 ÷ 5 = 1 remainder 2 |
| 9 | 5 ÷ 2 = 2 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 49 and 182 | 1274 |
| 80 and 157 | 12560 |
| 131 and 160 | 20960 |
| 185 and 192 | 35520 |
| 105 and 30 | 210 |