Least Common Multiple (LCM) of 129 and 75
The least common multiple (LCM) of 129 and 75 is 3225.
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 75?
First, calculate the GCD of 129 and 75 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 75 = 1 remainder 54 |
| 2 | 75 ÷ 54 = 1 remainder 21 |
| 3 | 54 ÷ 21 = 2 remainder 12 |
| 4 | 21 ÷ 12 = 1 remainder 9 |
| 5 | 12 ÷ 9 = 1 remainder 3 |
| 6 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 66 | 264 |
| 68 and 103 | 7004 |
| 135 and 175 | 4725 |
| 70 and 131 | 9170 |
| 116 and 200 | 5800 |