Least Common Multiple (LCM) of 18 and 122
The least common multiple (LCM) of 18 and 122 is 1098.
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 18 and 122?
First, calculate the GCD of 18 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 122 = 0 remainder 18 |
| 2 | 122 ÷ 18 = 6 remainder 14 |
| 3 | 18 ÷ 14 = 1 remainder 4 |
| 4 | 14 ÷ 4 = 3 remainder 2 |
| 5 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 123 and 76 | 9348 |
| 117 and 120 | 4680 |
| 41 and 197 | 8077 |
| 185 and 115 | 4255 |
| 34 and 135 | 4590 |