Least Common Multiple (LCM) of 107 and 122
The least common multiple (LCM) of 107 and 122 is 13054.
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 122?
First, calculate the GCD of 107 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 122 = 0 remainder 107 |
| 2 | 122 ÷ 107 = 1 remainder 15 |
| 3 | 107 ÷ 15 = 7 remainder 2 |
| 4 | 15 ÷ 2 = 7 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 12 | 516 |
| 10 and 189 | 1890 |
| 29 and 87 | 87 |
| 39 and 88 | 3432 |
| 68 and 68 | 68 |