Least Common Multiple (LCM) of 129 and 173
The least common multiple (LCM) of 129 and 173 is 22317.
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 173?
First, calculate the GCD of 129 and 173 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 173 = 0 remainder 129 |
| 2 | 173 ÷ 129 = 1 remainder 44 |
| 3 | 129 ÷ 44 = 2 remainder 41 |
| 4 | 44 ÷ 41 = 1 remainder 3 |
| 5 | 41 ÷ 3 = 13 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 153 and 189 | 3213 |
| 96 and 62 | 2976 |
| 174 and 190 | 16530 |
| 18 and 182 | 1638 |
| 115 and 42 | 4830 |