Least Common Multiple (LCM) of 105 and 122
The least common multiple (LCM) of 105 and 122 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 105 and 122?
First, calculate the GCD of 105 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 122 = 0 remainder 105 |
| 2 | 122 ÷ 105 = 1 remainder 17 |
| 3 | 105 ÷ 17 = 6 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 90 | 9090 |
| 82 and 78 | 3198 |
| 128 and 149 | 19072 |
| 159 and 171 | 9063 |
| 99 and 133 | 13167 |