Least Common Multiple (LCM) of 107 and 129
The least common multiple (LCM) of 107 and 129 is 13803.
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 107 and 129?
First, calculate the GCD of 107 and 129 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 129 = 0 remainder 107 |
| 2 | 129 ÷ 107 = 1 remainder 22 |
| 3 | 107 ÷ 22 = 4 remainder 19 |
| 4 | 22 ÷ 19 = 1 remainder 3 |
| 5 | 19 ÷ 3 = 6 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 189 and 58 | 10962 |
| 20 and 33 | 660 |
| 150 and 88 | 6600 |
| 73 and 25 | 1825 |
| 99 and 161 | 15939 |