Least Common Multiple (LCM) of 129 and 79
The least common multiple (LCM) of 129 and 79 is 10191.
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 79?
First, calculate the GCD of 129 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 79 = 1 remainder 50 |
| 2 | 79 ÷ 50 = 1 remainder 29 |
| 3 | 50 ÷ 29 = 1 remainder 21 |
| 4 | 29 ÷ 21 = 1 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 59 and 143 | 8437 |
| 199 and 137 | 27263 |
| 173 and 59 | 10207 |
| 105 and 92 | 9660 |
| 107 and 164 | 17548 |