Least Common Multiple (LCM) of 129 and 34
The least common multiple (LCM) of 129 and 34 is 4386.
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 34?
First, calculate the GCD of 129 and 34 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 34 = 3 remainder 27 |
| 2 | 34 ÷ 27 = 1 remainder 7 |
| 3 | 27 ÷ 7 = 3 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 59 | 8555 |
| 174 and 61 | 10614 |
| 96 and 182 | 8736 |
| 120 and 98 | 5880 |
| 183 and 182 | 33306 |