Least Common Multiple (LCM) of 81 and 127
The least common multiple (LCM) of 81 and 127 is 10287.
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 127?
First, calculate the GCD of 81 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 81 ÷ 127 = 0 remainder 81 |
| 2 | 127 ÷ 81 = 1 remainder 46 |
| 3 | 81 ÷ 46 = 1 remainder 35 |
| 4 | 46 ÷ 35 = 1 remainder 11 |
| 5 | 35 ÷ 11 = 3 remainder 2 |
| 6 | 11 ÷ 2 = 5 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 177 | 29559 |
| 131 and 91 | 11921 |
| 115 and 131 | 15065 |
| 186 and 85 | 15810 |
| 160 and 29 | 4640 |