Least Common Multiple (LCM) of 103 and 127
The least common multiple (LCM) of 103 and 127 is 13081.
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 103 and 127?
First, calculate the GCD of 103 and 127 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 127 = 0 remainder 103 |
| 2 | 127 ÷ 103 = 1 remainder 24 |
| 3 | 103 ÷ 24 = 4 remainder 7 |
| 4 | 24 ÷ 7 = 3 remainder 3 |
| 5 | 7 ÷ 3 = 2 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 142 | 18886 |
| 148 and 138 | 10212 |
| 119 and 190 | 22610 |
| 158 and 186 | 14694 |
| 187 and 86 | 16082 |