Least Common Multiple (LCM) of 10 and 129
The least common multiple (LCM) of 10 and 129 is 1290.
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 10 and 129?
First, calculate the GCD of 10 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 10 ÷ 129 = 0 remainder 10 |
| 2 | 129 ÷ 10 = 12 remainder 9 |
| 3 | 10 ÷ 9 = 1 remainder 1 |
| 4 | 9 ÷ 1 = 9 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 169 | 21801 |
| 185 and 77 | 14245 |
| 193 and 62 | 11966 |
| 135 and 118 | 15930 |
| 57 and 131 | 7467 |