Least Common Multiple (LCM) of 129 and 84
The least common multiple (LCM) of 129 and 84 is 3612.
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 84?
First, calculate the GCD of 129 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 84 = 1 remainder 45 |
| 2 | 84 ÷ 45 = 1 remainder 39 |
| 3 | 45 ÷ 39 = 1 remainder 6 |
| 4 | 39 ÷ 6 = 6 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 75 and 31 | 2325 |
| 30 and 101 | 3030 |
| 148 and 91 | 13468 |
| 45 and 54 | 270 |
| 169 and 127 | 21463 |