Least Common Multiple (LCM) of 188 and 129
The least common multiple (LCM) of 188 and 129 is 24252.
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 188 and 129?
First, calculate the GCD of 188 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 188 ÷ 129 = 1 remainder 59 |
| 2 | 129 ÷ 59 = 2 remainder 11 |
| 3 | 59 ÷ 11 = 5 remainder 4 |
| 4 | 11 ÷ 4 = 2 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 75 | 1275 |
| 34 and 60 | 1020 |
| 116 and 79 | 9164 |
| 45 and 94 | 4230 |
| 158 and 71 | 11218 |