Least Common Multiple (LCM) of 108 and 122
The least common multiple (LCM) of 108 and 122 is 6588.
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 108 and 122?
First, calculate the GCD of 108 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 122 = 0 remainder 108 |
| 2 | 122 ÷ 108 = 1 remainder 14 |
| 3 | 108 ÷ 14 = 7 remainder 10 |
| 4 | 14 ÷ 10 = 1 remainder 4 |
| 5 | 10 ÷ 4 = 2 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 113 and 75 | 8475 |
| 69 and 12 | 276 |
| 122 and 188 | 11468 |
| 67 and 153 | 10251 |
| 178 and 136 | 12104 |