Least Common Multiple (LCM) of 129 and 45
The least common multiple (LCM) of 129 and 45 is 1935.
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 45?
First, calculate the GCD of 129 and 45 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 45 = 2 remainder 39 |
| 2 | 45 ÷ 39 = 1 remainder 6 |
| 3 | 39 ÷ 6 = 6 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 136 and 51 | 408 |
| 101 and 196 | 19796 |
| 76 and 79 | 6004 |
| 100 and 86 | 4300 |
| 96 and 50 | 2400 |