Least Common Multiple (LCM) of 129 and 59
The least common multiple (LCM) of 129 and 59 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 129 and 59?
First, calculate the GCD of 129 and 59 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 59 = 2 remainder 11 |
| 2 | 59 ÷ 11 = 5 remainder 4 |
| 3 | 11 ÷ 4 = 2 remainder 3 |
| 4 | 4 ÷ 3 = 1 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 111 | 15540 |
| 131 and 81 | 10611 |
| 160 and 70 | 1120 |
| 129 and 34 | 4386 |
| 19 and 57 | 57 |