Least Common Multiple (LCM) of 179 and 129
The least common multiple (LCM) of 179 and 129 is 23091.
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 179 and 129?
First, calculate the GCD of 179 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 129 = 1 remainder 50 |
| 2 | 129 ÷ 50 = 2 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 |
|---|---|
| 56 and 57 | 3192 |
| 73 and 168 | 12264 |
| 90 and 197 | 17730 |
| 29 and 21 | 609 |
| 174 and 97 | 16878 |