Least Common Multiple (LCM) of 129 and 198
The least common multiple (LCM) of 129 and 198 is 8514.
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 198?
First, calculate the GCD of 129 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 198 = 0 remainder 129 |
| 2 | 198 ÷ 129 = 1 remainder 69 |
| 3 | 129 ÷ 69 = 1 remainder 60 |
| 4 | 69 ÷ 60 = 1 remainder 9 |
| 5 | 60 ÷ 9 = 6 remainder 6 |
| 6 | 9 ÷ 6 = 1 remainder 3 |
| 7 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 37 and 14 | 518 |
| 69 and 116 | 8004 |
| 170 and 15 | 510 |
| 100 and 108 | 2700 |
| 171 and 38 | 342 |