Least Common Multiple (LCM) of 82 and 127
The least common multiple (LCM) of 82 and 127 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 82 and 127?
First, calculate the GCD of 82 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 82 ÷ 127 = 0 remainder 82 |
| 2 | 127 ÷ 82 = 1 remainder 45 |
| 3 | 82 ÷ 45 = 1 remainder 37 |
| 4 | 45 ÷ 37 = 1 remainder 8 |
| 5 | 37 ÷ 8 = 4 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 64 and 51 | 3264 |
| 138 and 113 | 15594 |
| 168 and 47 | 7896 |
| 159 and 150 | 7950 |
| 179 and 114 | 20406 |