Least Common Multiple (LCM) of 198 and 122
The least common multiple (LCM) of 198 and 122 is 12078.
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 198 and 122?
First, calculate the GCD of 198 and 122 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 198 ÷ 122 = 1 remainder 76 |
| 2 | 122 ÷ 76 = 1 remainder 46 |
| 3 | 76 ÷ 46 = 1 remainder 30 |
| 4 | 46 ÷ 30 = 1 remainder 16 |
| 5 | 30 ÷ 16 = 1 remainder 14 |
| 6 | 16 ÷ 14 = 1 remainder 2 |
| 7 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 64 | 960 |
| 68 and 52 | 884 |
| 23 and 159 | 3657 |
| 22 and 37 | 814 |
| 146 and 46 | 3358 |