Least Common Multiple (LCM) of 107 and 127
The least common multiple (LCM) of 107 and 127 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 107 and 127?
First, calculate the GCD of 107 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 127 = 0 remainder 107 |
| 2 | 127 ÷ 107 = 1 remainder 20 |
| 3 | 107 ÷ 20 = 5 remainder 7 |
| 4 | 20 ÷ 7 = 2 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 44 and 37 | 1628 |
| 52 and 159 | 8268 |
| 105 and 169 | 17745 |
| 43 and 138 | 5934 |
| 121 and 169 | 20449 |