Least Common Multiple (LCM) of 129 and 110
The least common multiple (LCM) of 129 and 110 is 14190.
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 110?
First, calculate the GCD of 129 and 110 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 110 = 1 remainder 19 |
| 2 | 110 ÷ 19 = 5 remainder 15 |
| 3 | 19 ÷ 15 = 1 remainder 4 |
| 4 | 15 ÷ 4 = 3 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 197 and 172 | 33884 |
| 108 and 22 | 1188 |
| 78 and 171 | 4446 |
| 198 and 39 | 2574 |
| 184 and 87 | 16008 |