Least Common Multiple (LCM) of 79 and 129
The least common multiple (LCM) of 79 and 129 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 79 and 129?
First, calculate the GCD of 79 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 79 ÷ 129 = 0 remainder 79 |
| 2 | 129 ÷ 79 = 1 remainder 50 |
| 3 | 79 ÷ 50 = 1 remainder 29 |
| 4 | 50 ÷ 29 = 1 remainder 21 |
| 5 | 29 ÷ 21 = 1 remainder 8 |
| 6 | 21 ÷ 8 = 2 remainder 5 |
| 7 | 8 ÷ 5 = 1 remainder 3 |
| 8 | 5 ÷ 3 = 1 remainder 2 |
| 9 | 3 ÷ 2 = 1 remainder 1 |
| 10 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 196 | 15876 |
| 194 and 26 | 2522 |
| 41 and 196 | 8036 |
| 145 and 141 | 20445 |
| 112 and 79 | 8848 |