Least Common Multiple (LCM) of 108 and 127
The least common multiple (LCM) of 108 and 127 is 13716.
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 108 and 127?
First, calculate the GCD of 108 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 127 = 0 remainder 108 |
| 2 | 127 ÷ 108 = 1 remainder 19 |
| 3 | 108 ÷ 19 = 5 remainder 13 |
| 4 | 19 ÷ 13 = 1 remainder 6 |
| 5 | 13 ÷ 6 = 2 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 87 and 99 | 2871 |
| 140 and 28 | 140 |
| 194 and 97 | 194 |
| 200 and 83 | 16600 |
| 133 and 38 | 266 |