Least Common Multiple (LCM) of 127 and 107
The least common multiple (LCM) of 127 and 107 is 13589.
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 107?
First, calculate the GCD of 127 and 107 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 127 ÷ 107 = 1 remainder 20 |
| 2 | 107 ÷ 20 = 5 remainder 7 |
| 3 | 20 ÷ 7 = 2 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 166 and 41 | 6806 |
| 110 and 177 | 19470 |
| 37 and 110 | 4070 |
| 138 and 97 | 13386 |
| 149 and 58 | 8642 |