Least Common Multiple (LCM) of 110 and 129
The least common multiple (LCM) of 110 and 129 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 110 and 129?
First, calculate the GCD of 110 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 110 ÷ 129 = 0 remainder 110 |
| 2 | 129 ÷ 110 = 1 remainder 19 |
| 3 | 110 ÷ 19 = 5 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 162 | 6966 |
| 185 and 102 | 18870 |
| 137 and 113 | 15481 |
| 177 and 119 | 21063 |
| 14 and 35 | 70 |