Least Common Multiple (LCM) of 127 and 82
The least common multiple (LCM) of 127 and 82 is 10414.
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 82?
First, calculate the GCD of 127 and 82 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 82 = 1 remainder 45 |
| 2 | 82 ÷ 45 = 1 remainder 37 |
| 3 | 45 ÷ 37 = 1 remainder 8 |
| 4 | 37 ÷ 8 = 4 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 187 | 13277 |
| 81 and 17 | 1377 |
| 56 and 196 | 392 |
| 106 and 132 | 6996 |
| 54 and 159 | 2862 |