Least Common Multiple (LCM) of 122 and 198
The least common multiple (LCM) of 122 and 198 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 122 and 198?
First, calculate the GCD of 122 and 198 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 122 ÷ 198 = 0 remainder 122 |
| 2 | 198 ÷ 122 = 1 remainder 76 |
| 3 | 122 ÷ 76 = 1 remainder 46 |
| 4 | 76 ÷ 46 = 1 remainder 30 |
| 5 | 46 ÷ 30 = 1 remainder 16 |
| 6 | 30 ÷ 16 = 1 remainder 14 |
| 7 | 16 ÷ 14 = 1 remainder 2 |
| 8 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 168 | 2520 |
| 145 and 76 | 11020 |
| 26 and 68 | 884 |
| 129 and 169 | 21801 |
| 105 and 90 | 630 |