Least Common Multiple (LCM) of 122 and 105
The least common multiple (LCM) of 122 and 105 is 12810.
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 122 and 105?
First, calculate the GCD of 122 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 105 = 1 remainder 17 |
| 2 | 105 ÷ 17 = 6 remainder 3 |
| 3 | 17 ÷ 3 = 5 remainder 2 |
| 4 | 3 ÷ 2 = 1 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 129 and 103 | 13287 |
| 182 and 18 | 1638 |
| 83 and 85 | 7055 |
| 194 and 10 | 970 |
| 159 and 165 | 8745 |