Least Common Multiple (LCM) of 75 and 129
The least common multiple (LCM) of 75 and 129 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 75 and 129?
First, calculate the GCD of 75 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 75 ÷ 129 = 0 remainder 75 |
| 2 | 129 ÷ 75 = 1 remainder 54 |
| 3 | 75 ÷ 54 = 1 remainder 21 |
| 4 | 54 ÷ 21 = 2 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 197 | 35854 |
| 13 and 174 | 2262 |
| 75 and 114 | 2850 |
| 116 and 179 | 20764 |
| 65 and 111 | 7215 |