Least Common Multiple (LCM) of 45 and 129
The least common multiple (LCM) of 45 and 129 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 45 and 129?
First, calculate the GCD of 45 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 129 = 0 remainder 45 |
| 2 | 129 ÷ 45 = 2 remainder 39 |
| 3 | 45 ÷ 39 = 1 remainder 6 |
| 4 | 39 ÷ 6 = 6 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 20 and 83 | 1660 |
| 17 and 38 | 646 |
| 65 and 26 | 130 |
| 122 and 74 | 4514 |
| 75 and 51 | 1275 |