Least Common Multiple (LCM) of 129 and 101
The least common multiple (LCM) of 129 and 101 is 13029.
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 101?
First, calculate the GCD of 129 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 101 = 1 remainder 28 |
| 2 | 101 ÷ 28 = 3 remainder 17 |
| 3 | 28 ÷ 17 = 1 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 61 and 67 | 4087 |
| 34 and 72 | 1224 |
| 169 and 35 | 5915 |
| 57 and 174 | 3306 |
| 131 and 38 | 4978 |