Least Common Multiple (LCM) of 129 and 69
The least common multiple (LCM) of 129 and 69 is 2967.
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 69?
First, calculate the GCD of 129 and 69 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 69 = 1 remainder 60 |
| 2 | 69 ÷ 60 = 1 remainder 9 |
| 3 | 60 ÷ 9 = 6 remainder 6 |
| 4 | 9 ÷ 6 = 1 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 11 | 649 |
| 15 and 68 | 1020 |
| 112 and 87 | 9744 |
| 170 and 149 | 25330 |
| 27 and 103 | 2781 |