Least Common Multiple (LCM) of 59 and 129
The least common multiple (LCM) of 59 and 129 is 7611.
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 59 and 129?
First, calculate the GCD of 59 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 59 ÷ 129 = 0 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 |
|---|---|
| 112 and 158 | 8848 |
| 27 and 105 | 945 |
| 184 and 130 | 11960 |
| 86 and 75 | 6450 |
| 136 and 99 | 13464 |