Least Common Multiple (LCM) of 129 and 175
The least common multiple (LCM) of 129 and 175 is 22575.
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 175?
First, calculate the GCD of 129 and 175 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 129 ÷ 175 = 0 remainder 129 |
| 2 | 175 ÷ 129 = 1 remainder 46 |
| 3 | 129 ÷ 46 = 2 remainder 37 |
| 4 | 46 ÷ 37 = 1 remainder 9 |
| 5 | 37 ÷ 9 = 4 remainder 1 |
| 6 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 54 | 3024 |
| 35 and 24 | 840 |
| 103 and 128 | 13184 |
| 157 and 99 | 15543 |
| 58 and 104 | 3016 |