Least Common Multiple (LCM) of 173 and 129
The least common multiple (LCM) of 173 and 129 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 173 and 129?
First, calculate the GCD of 173 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 173 ÷ 129 = 1 remainder 44 |
| 2 | 129 ÷ 44 = 2 remainder 41 |
| 3 | 44 ÷ 41 = 1 remainder 3 |
| 4 | 41 ÷ 3 = 13 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 126 | 3276 |
| 105 and 115 | 2415 |
| 108 and 87 | 3132 |
| 122 and 34 | 2074 |
| 75 and 129 | 3225 |