Least Common Multiple (LCM) of 135 and 129
The least common multiple (LCM) of 135 and 129 is 5805.
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 135 and 129?
First, calculate the GCD of 135 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 135 ÷ 129 = 1 remainder 6 |
| 2 | 129 ÷ 6 = 21 remainder 3 |
| 3 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 24 | 2760 |
| 140 and 102 | 7140 |
| 191 and 33 | 6303 |
| 104 and 198 | 10296 |
| 198 and 82 | 8118 |