Least Common Multiple (LCM) of 127 and 81
The least common multiple (LCM) of 127 and 81 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 127 and 81?
First, calculate the GCD of 127 and 81 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 81 = 1 remainder 46 |
| 2 | 81 ÷ 46 = 1 remainder 35 |
| 3 | 46 ÷ 35 = 1 remainder 11 |
| 4 | 35 ÷ 11 = 3 remainder 2 |
| 5 | 11 ÷ 2 = 5 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 82 | 1230 |
| 21 and 45 | 315 |
| 12 and 105 | 420 |
| 118 and 98 | 5782 |
| 10 and 15 | 30 |