Least Common Multiple (LCM) of 129 and 54
The least common multiple (LCM) of 129 and 54 is 2322.
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 54?
First, calculate the GCD of 129 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 54 = 2 remainder 21 |
| 2 | 54 ÷ 21 = 2 remainder 12 |
| 3 | 21 ÷ 12 = 1 remainder 9 |
| 4 | 12 ÷ 9 = 1 remainder 3 |
| 5 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 190 and 59 | 11210 |
| 121 and 30 | 3630 |
| 186 and 158 | 14694 |
| 114 and 167 | 19038 |
| 138 and 40 | 2760 |