Least Common Multiple (LCM) of 129 and 83
The least common multiple (LCM) of 129 and 83 is 10707.
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 83?
First, calculate the GCD of 129 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 83 = 1 remainder 46 |
| 2 | 83 ÷ 46 = 1 remainder 37 |
| 3 | 46 ÷ 37 = 1 remainder 9 |
| 4 | 37 ÷ 9 = 4 remainder 1 |
| 5 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 100 | 2400 |
| 125 and 23 | 2875 |
| 47 and 20 | 940 |
| 120 and 153 | 6120 |
| 132 and 115 | 15180 |