Least Common Multiple (LCM) of 129 and 135
The least common multiple (LCM) of 129 and 135 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 129 and 135?
First, calculate the GCD of 129 and 135 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 135 = 0 remainder 129 |
| 2 | 135 ÷ 129 = 1 remainder 6 |
| 3 | 129 ÷ 6 = 21 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 130 | 7020 |
| 112 and 139 | 15568 |
| 167 and 60 | 10020 |
| 50 and 137 | 6850 |
| 170 and 141 | 23970 |