Least Common Multiple (LCM) of 129 and 103
The least common multiple (LCM) of 129 and 103 is 13287.
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 129 and 103?
First, calculate the GCD of 129 and 103 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 103 = 1 remainder 26 |
| 2 | 103 ÷ 26 = 3 remainder 25 |
| 3 | 26 ÷ 25 = 1 remainder 1 |
| 4 | 25 ÷ 1 = 25 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 186 and 72 | 2232 |
| 85 and 75 | 1275 |
| 70 and 106 | 3710 |
| 70 and 126 | 630 |
| 85 and 85 | 85 |