Least Common Multiple (LCM) of 117 and 129
The least common multiple (LCM) of 117 and 129 is 5031.
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 117 and 129?
First, calculate the GCD of 117 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 129 = 0 remainder 117 |
| 2 | 129 ÷ 117 = 1 remainder 12 |
| 3 | 117 ÷ 12 = 9 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 103 and 49 | 5047 |
| 112 and 129 | 14448 |
| 122 and 43 | 5246 |
| 153 and 190 | 29070 |
| 71 and 200 | 14200 |