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 |
|---|---|
| 199 and 172 | 34228 |
| 73 and 79 | 5767 |
| 111 and 147 | 5439 |
| 75 and 180 | 900 |
| 43 and 117 | 5031 |