Least Common Multiple (LCM) of 105 and 129
The least common multiple (LCM) of 105 and 129 is 4515.
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 105 and 129?
First, calculate the GCD of 105 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 129 = 0 remainder 105 |
| 2 | 129 ÷ 105 = 1 remainder 24 |
| 3 | 105 ÷ 24 = 4 remainder 9 |
| 4 | 24 ÷ 9 = 2 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 97 | 19109 |
| 178 and 50 | 4450 |
| 141 and 26 | 3666 |
| 63 and 20 | 1260 |
| 123 and 151 | 18573 |