Least Common Multiple (LCM) of 129 and 144
The least common multiple (LCM) of 129 and 144 is 6192.
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 144?
First, calculate the GCD of 129 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 144 = 0 remainder 129 |
| 2 | 144 ÷ 129 = 1 remainder 15 |
| 3 | 129 ÷ 15 = 8 remainder 9 |
| 4 | 15 ÷ 9 = 1 remainder 6 |
| 5 | 9 ÷ 6 = 1 remainder 3 |
| 6 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 18 and 104 | 936 |
| 11 and 106 | 1166 |
| 198 and 122 | 12078 |
| 112 and 164 | 4592 |
| 109 and 59 | 6431 |