Least Common Multiple (LCM) of 34 and 129
The least common multiple (LCM) of 34 and 129 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 34 and 129?
First, calculate the GCD of 34 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 34 ÷ 129 = 0 remainder 34 |
| 2 | 129 ÷ 34 = 3 remainder 27 |
| 3 | 34 ÷ 27 = 1 remainder 7 |
| 4 | 27 ÷ 7 = 3 remainder 6 |
| 5 | 7 ÷ 6 = 1 remainder 1 |
| 6 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 156 | 6240 |
| 39 and 91 | 273 |
| 157 and 129 | 20253 |
| 171 and 174 | 9918 |
| 20 and 18 | 180 |